Ergodic and qualitative theories of dynamical systems II

• Grant number: 19/10269-3
• Support Opportunities: Research Projects - Thematic Grants
• Start date: August 01, 2019
• End date: July 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Claudio Aguinaldo Buzzi
• Grantee: Claudio Aguinaldo Buzzi
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• Pesquisadores principais: Ali Messaoudi ; Paulo Ricardo da Silva
• Associated researchers: Benito Frazao Pires ; Cláudio Gomes Pessoa ; Douglas Duarte Novaes ; Eduardo Garibaldi ; Marcelo Messias ; Márcio Ricardo Alves Gouveia ; Maurício Firmino Silva Lima ; Patricia Romano Cirilo ; Pedro Toniol Cardin ; Sylvain Philippe Pierre Bonnot ; Tiago de Carvalho ; Vanderlei Minori Horita
• Associated research grant(s): 23/09466-4 - Periodic orbits in some piecewise differential systems, AV.EXT; 23/04949-7 - 3rd International Nonlinear Dynamics Conference (NODYCON 2023), AR.EXT; 22/13362-7 - Advances in Qualitative Theory of Differential Equations 2023, AR.EXT
• Associated scholarship(s): 24/07448-1 - Dynamic of Exchange maps and Rauzy Fractals, BP.MS; 24/02471-5 - A study of differential equations with application to beam deflection, BP.IC; 23/06371-2 - Several Aspects of Discrete Dynamics, BP.PD; + associated scholarships 23/05469-9 - Introduction to the Qualitative Theory of Ordinary Differential Equations, BP.IC; 22/10534-1 - Introduction to the qualitative theory of ordinary differential equations and applications, BP.IC; 21/01799-9 - The study of vector fields with applications at game theory, BP.DR; 21/00193-0 - About the number of limit cycles that bifurcate from a linear center, BP.IC; 20/06708-9 - Piecewise Holomorphic Systems and Regularization of Filippov fields around degenerated singularities and regular tangential polycycles, BP.PD; 20/10386-7 - Introduction to piecewise smooth dynamical systems and applications, BP.IC; 20/08906-2 - Nonlinear ordinary differential equations: a first study, BP.IC; 20/04717-0 - Dynamical systems with symmetries and implicit differential equations, BP.PD; 19/13040-7 - Nilpotent centers on the center manifolds, BP.DR; 19/20500-4 - Abundance of transitive linear operators in infinite dimension, BP.MS - associated scholarships

Abstract

This project is a continuation of the thematic project: Ergodic and Qualitative Theories of Dynamical Systems (process 2013 / 24541-0). Our goal is to study several problems in the area of dynamical systems and their connections with other areas such as Analysis, Ergodic Theory, Number Theory, Topology among many others. The problems to be addressed are current and include the following topics: Julia sets, infinite matrix dynamics, shadowing, structural stability and ergodicity in linear dynamics, topological dynamics of the composition operator, systems with multiple scales and implicit differential equations, regularization of discontinuous foliations, singular polynomial perturbations, contact partially hyperbolic skew-products, fractal dimensions of non-uniformly expanding repellers, low-discrete KAM solutions for quasi-crystalline interaction models, structural stability, minimality and regularization of non-smooth systems, Thom-Smale program in foliated manifolds, cyclicity and the center-focus problem in three-dimensional manifolds. The main institution is UNESP - S. J. Rio Preto. The team consists of researchers with experience in doctoral supervising and leading research project teams, as well as young researchers. The team has also members from other campuses of UNESP: Ilha Solteira and Presidente Prudente, as well as other institutions of São Paulo State: UNIFESP (São José dos Campos), IME-USP, IMECC-UNICAMP, USP-Ribeirão Preto and UFABC. The project will be guided by the following actions: i) cooperation with high level researches from Brazil and other countries as France, Spain, England, USA, Austria, Chile and Uruguay; ii) participation in conferences and visits to renowned research centers; iii) publication of results in high level scientific journals; iv) training and qualification of human resources in mathematics. (AU)

Scientific publications

(98)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

LLIBRE, JAUME; PEREIRA, WEBER F.; PESSOA, CLAUDIO. PHASE PORTRAITS OF BERNOULLI QUADRATIC POLYNOMIAL DIFFERENTIAL SYSTEMS. Electronic Journal of Differential Equations, p. 1-19, MAY 22 2020. (18/19726-5, 19/10269-3)

CARVALHO, TIAGO; GONCALVES, LUIZ FERNANDO. Creation of Limit Cycles in Piecewise Smooth Vector Fields Tangent to Nested Tori. Qualitative Theory of Dynamical Systems, v. 20, n. 2, p. 21-pg., 2021-07-01. (19/10269-3, 19/10450-0)

CARMONA, VICTORIANO; FERNANDEZ-SANCHEZ, FERNANDO; NOVAES, DOUGLAS D.. A Succinct Characterization of Period Annuli in Planar Piecewise Linear Differential Systems with a Straight Line of Nonsmoothness. JOURNAL OF NONLINEAR SCIENCE, v. 33, n. 5, p. 13-pg., 2023-10-01. (19/10269-3, 21/10606-0, 18/13481-0, 22/09633-5)

BUZZI, CLAUDIO A.; ROMANO CARVALHO, YAGOR; GASULL, ARMENGOL. Limit cycles for some families of smooth and non-smooth planar systems. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 207, JUN 2021. (16/00242-2, 18/05098-2, 19/10269-3)

MESSIAS, MARCELO; REINOL, ALISSON C.. The Occurrence of Zero-Hopf Bifurcation in a Generalized Sprott A System. NONLINEAR DYNAMICS OF STRUCTURES, SYSTEMS AND DEVICES, VOL I, NODYCON 2019, v. N/A, p. 9-pg., 2020-01-01. (19/10269-3)

SANTANA, PAULO. On the structural instability of non-hyperbolic limit cycles on planar polynomial vector fields. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, v. N/A, p. 14-pg., 2024-05-20. (22/14353-1, 21/01799-9, 19/10269-3)

PESSOA, CLAUDIO; RIBEIRO, RONISIO. Bifurcation of limit cycles from a periodic annulus formed by a center and two saddles in piecewise linear differential system with three zones. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, v. 80, p. 17-pg., 2024-06-27. (19/10269-3, 23/04061-6)

GOUVEIA, MARCIO R. A.; LLIBRE, JAUME; ROBERTO, LUCI ANY. Phase Portraits of a Family of Hamiltonian Cubic Systems. DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS, v. N/A, p. 9-pg., 2024-04-05. (22/04040-6, 19/10269-3)

ANTUNES, A. A.; CARVALHO, T.; GOMIDE, O. M. L.. Closing Lemma for piecewise smooth vector fields with a recurrent point. NONLINEAR ANALYSIS-HYBRID SYSTEMS, v. 53, p. 9-pg., 2024-04-09. (19/10450-0, 17/18255-6, 21/12395-6, 19/10269-3, 22/02819-6)

CAPRIO, DANILO A.; MESSAOUDI, ALI; VALLE, GLAUCO. STOCHASTIC ADDING MACHINES BASED ON BRATTELI DIAGRAMS. ANNALES DE L INSTITUT FOURIER, v. 70, n. 6, p. 39-pg., 2020-01-01. (19/10269-3, 15/26161-6)

CARVALHO, TIAGO; GONCALVES, LUIZ FERNANDO. A FLOW ON S-2 PRESENTING THE BALL AS ITS MINIMAL SET. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, v. 26, n. 8, p. 18-pg., 2021-08-01. (19/10269-3, 19/10450-0)

DOMINGOS, WEBERTY; FERENCZI, SEBASTIEN; MESSAOUDI, ALI; VALLE, GLAUCO. Invariant measures for substitutions on countable alphabets. Ergodic Theory and Dynamical Systems, v. 44, n. 9, p. 32-pg., 2023-12-11. (19/10269-3)

LLIBRE, JAUME; NOVAES, DOUGLAS D.; VALLS, CLAUDIA. Existence of a cylinder foliated by periodic orbits in the generalized Chazy differential equation. Chaos, v. 33, n. 7, p. 17-pg., 2023-07-01. (18/13481-0, 21/10606-0, 19/10269-3, 22/09633-5)

LLIBRE, JAUME; SANTANA, PAULO. Limit cycles and chaos in planar hybrid systems. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 140, p. 13-pg., 2024-10-09. (22/14353-1, 21/01799-9, 19/10269-3)

PESSOA, CLAUDIO; RIBEIRO, RONISIO. Limit cycles of planar piecewise linear Hamiltonian differential systems with two or three zones. Electronic Journal of Qualitative Theory of Differential Equations, v. N/A, n. 27, p. 19-pg., 2022-01-01. (18/19726-5, 19/10269-3)

LLIBRE, JAUME; PEREIRA, WEBER F.; PESSOA, CLAUDIO. PHASE PORTRAITS OF BERNOULLI QUADRATIC POLYNOMIAL DIFFERENTIAL SYSTEMS. Electronic Journal of Differential Equations, v. N/A, p. 19-pg., 2020-05-22. (18/19726-5, 19/10269-3)

CARMONA, VICTORIANO; FERNANDEZ-SANCHEZ, FERNANDO; NOVAES, DOUGLAS D.. Uniqueness and stability of limit cycles in planar piecewise linear differential systems without sliding region. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 123, p. 18-pg., 2023-04-28. (19/10269-3, 21/10606-0, 18/13481-0, 22/09633-5)

ANDRADE, KAMILA S.; GOMIDE, OTAVIO M. L.; NOVAES, DOUGLAS D.. Bifurcation diagrams of global connections in Filippov systems. NONLINEAR ANALYSIS-HYBRID SYSTEMS, v. 50, p. 26-pg., 2023-11-01. (19/10269-3, 18/13481-0, 15/22762-5, 22/09633-5)

PESSOA, CLAUDIO; RIBEIRO, RONISIO; NOVAES, DOUGLAS; GOUVEIA, MARCIO; EUZEBIO, RODRIGO. On cyclicity in discontinuous piecewise linear near-Hamiltonian differential systems with three zones having a saddle in the central one. NONLINEAR DYNAMICS, v. 111, n. 22, p. 23-pg., 2023-11-01. (22/04040-6, 18/13481-0, 19/10269-3, 23/04061-6, 22/09633-5)

PIRES, BENITO. Lyapunov function for interacting reinforced stochastic processes via Hopfield's energy function. Statistics & Probability Letters, v. 205, p. 6-pg., 2023-11-01. (19/10269-3, 22/14130-2)

PEREZ, OTAVIO HENRIQUE; DA SILVA, PAULO RICARDO. Polynomial slow-fast systems on the Poincaré-Lyapunov sphere. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, v. N/A, p. 26-pg., 2024-06-24. (23/02959-5, 21/10198-9, 19/10269-3)

PEREZ, OTAVIO HENRIQUE; DA SILVA, PAULO RICARDO. Resolution of singularities of 2-dimensional real analytic constrained differential systems. BULLETIN DES SCIENCES MATHEMATIQUES, v. 179, p. 31-pg., 2022-08-09. (18/24692-2, 19/10269-3, 16/22310-0)

BUZZI, CLAUDIO A.; CARVALHO, YAGOR ROMANO; LLIBRE, JAUME. Crossing limit cycles of planar discontinuous piecewise differential systems formed by isochronous centres. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, v. 37, n. 4, p. 19-pg., 2022-09-28. (21/14695-7, 16/00242-2, 19/10269-3, 18/05098-2)

NOVAES, DOUGLAS D.; RONDON, GABRIEL. Smoothing of nonsmooth differential systems near regular-tangential singularities and boundary limit cycles. Nonlinearity, v. 34, n. 6, p. 4202-4263, JUN 2021. (18/16430-8, 19/10269-3, 20/06708-9, 18/13481-0)

BUZZI, CLAUDIO A.; CARVALHO, YAGOR ROMANO; GASULL, ARMENGOL. The local period function for Hamiltonian systems with applications. Journal of Differential Equations, v. 280, p. 590-617, APR 15 2021. (19/10269-3, 16/00242-2, 18/05098-2)

MESSIAS, MARCELO; REINOL, ALISSON DE CARVALHO. ocal-Activity and Simultaneous Zero-Hopf Bifurcations Leading to Multistability in a Memristive Circui. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 31, n. 15, DEC 15 2021. (19/10269-3)

BUZZI, CLAUDIO A.; PESSOA, CLAUDIO; MEDRADO, JOAO C.. Monodromy and Dulac's problem for piecewise analytical planar vector fields. BULLETIN DES SCIENCES MATHEMATIQUES, v. 188, p. 27-pg., 2023-11-01. (18/19726-5, 19/10269-3)

CARVALHO, TIAGO; FREITAS, BRUNO RODRIGUES. paper The local behavior around switching planes in a mathematical model to chemoimmunotherapy. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 120, p. 13-pg., 2023-06-01. (19/10269-3, 21/12395-6)

PESSOA, CLAUDIO; QUEIROZ, LUCAS; RIBEIRO, JARNE D.. Cyclicity of rigid centres on centre manifolds of three-dimensional systems. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, v. N/A, p. 13-pg., 2023-02-09. (18/19726-5, 19/10269-3, 19/13040-7)

CARVALHO, TIAGO; GONCALVES, LUIZ FERNANDO; LLIBRE, JAUME. On the Limit Cycles of a Class of Discontinuous Piecewise Differential Systems Formed by Two Rigid Centers Governed by Odd Degree Polynomials. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 32, n. 16, p. 11-pg., 2022-12-30.

GOUVEIA, LUIZ F. S.; RONDON, GABRIEL; SILVA, PAULO R. DA. Piecewise holomorphic systems. Journal of Differential Equations, v. 332, p. 33-pg., 2022-09-25. (20/04717-0, 20/06708-9, 19/10269-3)

ALVES, FABRICIO F.; BERNARDES JR, NILSON C.; MESSAOUDI, ALI. Chain recurrence and average shadowing in dynamics. MONATSHEFTE FUR MATHEMATIK, v. 196, n. 4, SEP 2021. (19/10269-3)

NOVAES, DOUGLAS D.; SILVA, LEANDRO A.. ON THE NON-EXISTENCE OF ISOCHRONOUS TANGENTIAL CENTERS IN FILIPPOV VECTOR FIELDS. Proceedings of the American Mathematical Society, v. 150, n. 12, p. 10-pg., 2022-07-01. (18/13481-0, 19/10269-3, 21/10606-0)

CARVALHO, TIAGO; CRISTIANO, RONY; RODRIGUES, DIEGO S.; TONON, DURVAL J.. Global Analysis of a piecewise smooth epidemiological model of COVID-19. NONLINEAR DYNAMICS, v. 105, n. 4, AUG 2021. (19/10269-3, 19/10450-0)

LLIBRE, JAUME; NOVAES, DOUGLAS D.; ZELI, IRIS O.. Limit cycles of piecewise polynomial perturbations of higher dimensional linear differential systems. REVISTA MATEMATICA IBEROAMERICANA, v. 36, n. 1, p. 291-318, 2020. (18/16430-8, 19/10269-3, 18/13481-0, 13/21078-8)

NOVAES, DOUGLAS D.; SEARA, TERE M.; TEIXEIRA, MARCO A.; ZELI, IRIS O.. Study of Periodic Orbits in Periodic Perturbations of Planar Reversible Filippov Systems Having a Twofold Cycle. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, v. 19, n. 2, p. 1343-1371, 2020. (18/13481-0, 13/21078-8, 19/10269-3)

MESSIAS, MARCELO; SILVA, RAFAEL PAULINO. Determination of Nonchaotic Behavior for Some Classes of Polynomial Jerk Equations. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 30, n. 8, JUN 30 2020. (19/10269-3)

LLIBRE, JAUME; PESSOA, CLAUDIO; RIBEIRO, JARNE D.. Rational first integrals of the Liénard equations: The solution to the Poincaré problem for the Liénard equations. Anais da Academia Brasileira de Ciências, v. 93, n. 4, 2021. (19/10269-3, 18/19726-5)

TONIOL CARDIN, PEDRO. Relaxation oscillation in planar discontinuous piecewise smooth fast-slow systems. Chaos, v. 32, n. 1, JAN 2022. (19/10269-3, 19/00976-4)

LLIBRE, JAUME; NOVAES, DOUGLAS D.; RODRIGUES, CAMILA A. B.. Bifurcations from families of periodic solutions in piecewise differential systems. PHYSICA D-NONLINEAR PHENOMENA, v. 404, MAR 2020. (18/16430-8, 18/13481-0, 19/10269-3)

CIRILO, PATRICIA; GOLLOBIT, BRYCE; PUJALS, ENRIQUE. Dynamics of generalized hyperbolic linear operators. ADVANCES IN MATHEMATICS, v. 387, AUG 27 2021. (19/10269-3, 19/09045-3)

BUZZI, CLAUDIO; LLIBRE, JAUME; SANTANA, PAULO. Phase portraits of (2;0) reversible vector fields with symmetrical singularities. Journal of Mathematical Analysis and Applications, v. 503, n. 2, NOV 15 2021. (18/23194-9, 19/10269-3, 19/21446-3)

IBRE, JAUME; MESSIAS, MARCELO; REINOL, ALISSON DE CARVALHO. Zero-Hopf Bifurcations in Three-Dimensional Chaotic Systems with One Stable Equilibrium. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 30, n. 13, OCT 2020. (19/10269-3)

CARMONA, VICTORIANO; FERNANDEZ-SANCHEZ, FERNANDO; NOVAES, DOUGLAS D.. A new simple proof for Lum-Chua's conjecture. NONLINEAR ANALYSIS-HYBRID SYSTEMS, v. 40, MAY 2021. (18/16430-8, 19/10269-3, 18/13481-0)

PEREZ, OTAVIO HENRIQUE; RONDON, GABRIEL; DA SILVA, PAULO RICARDO. Slow-Fast Normal Forms Arising from Piecewise Smooth Vector Fields. JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, v. N/A, p. 18-pg., 2023-07-17. (21/10198-9, 19/10269-3, 22/12123-9, 20/06708-9, 16/22310-0)

CANDIDO, MURILO R.; NOVAES, DOUGLAS D.. On the torus bifurcation in averaging theory. Journal of Differential Equations, v. 268, n. 8, p. 4555-4576, APR 5 2020. (18/07344-0, 19/05657-4, 18/16430-8, 18/13481-0, 19/10269-3)

CARDOSO, JOAO L.; LLIBRE, JAUME; NOVAES, DOUGLAS D.; TONON, DURVAL J.. Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, v. 35, n. 3, FEB 2020. (18/16430-8, 18/13481-0, 19/10269-3)

CARVALHO, TIAGO; NOVAES, DOUGLAS DUARTE; GONCALVES, LUIZ FERNANDO. Sliding Shilnikov connection in Filippov-type predator-prey model. NONLINEAR DYNAMICS, v. 100, n. 3, MAY 2020. (17/00883-0, 19/10450-0, 18/16430-8, 18/13481-0, 19/10269-3)

PESSOA, CLAUDIO; RIBEIRO, RONISIO. Persistence of periodic solutions from discontinuous planar piecewise linear Hamiltonian differential systems with three zones. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, v. 16, n. 2, p. 25-pg., 2022-07-11. (19/10269-3)

BERNARDES, JR., NILSON C.; MESSAOUDI, ALI. hadowing and structural stability for operator. Ergodic Theory and Dynamical Systems, v. 41, n. 4, p. 961-980, APR 2021. (19/10269-3, 17/22588-0)

PESSOA, CLAUDIO; RIBEIRO, RONISIO. Limit Cycles Bifurcating from a Periodic Annulus in Discontinuous Planar Piecewise Linear Hamiltonian Differential System with Three Zones. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 32, n. 08, p. 16-pg., 2022-06-30. (19/10269-3, 18/19726-5)

CANDIDO, MURILO R.; NOVAES, DOUGLAS D.; VALLS, CLAUDIA. Periodic solutions and invariant torus in the Rossler system. Nonlinearity, v. 33, n. 9, SEP 2020. (19/05657-4, 19/10269-3, 18/07344-0, 18/16430-8)

NOVAES, DOUGLAS D.. Higher order stroboscopic averaged functions: a general relationship with Melnikov functions. Electronic Journal of Qualitative Theory of Differential Equations, n. 77, 2021. (18/16430-8, 18/13481-0, 19/10269-3)

CASTRO, MATHEUS M.; MARTINS, RICARDO M.; NOVAES, DOUGLAS D.. Anote on Vishik's normal form. Journal of Differential Equations, v. 281, p. 442-458, APR 25 2021. (18/03338-6, 18/16430-8, 19/10269-3, 19/06873-2, 18/13481-0, 17/23692-6)

MAHDI, ADAM; PESSOA, CLAUDIO; RIBEIRO, JARNE D.. Rigid centres on the center manifold of tridimensional differential systems. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, v. N/A, p. 23-pg., 2021-09-07. (18/19726-5, 19/10269-3)

ROSALES, RAFAEL A. A.; PIRES, BENITO; PRADO, FERNANDO P. A.. Vertex reinforced random walks with exponential interaction on complete graphs. Stochastic Processes and their Applications, v. 148, p. 27-pg., 2022-06-01. (11/51509-5, 19/10269-3)

CARDIN, PEDRO TONIOL; NOVAES, DOUGLAS DUARTE. Asymptotic behavior of periodic solutions in one-parameter families of Lienard equations. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 190, JAN 2020. (19/00976-4, 18/13481-0, 19/10269-3, 13/24541-0, 18/16430-8)

BUZZI, CLAUDIO A.; RODERO, ANA LIVIA; TEIXEIRA, MARCO A.. Stability conditions for refractive partially integrable piecewise smooth vector fields. PHYSICA D-NONLINEAR PHENOMENA, v. 440, p. 15-pg., 2022-08-08. (18/13481-0, 19/10269-3, 19/00440-7, 17/08779-8)

NOVAES, DOUGLAS D.. AN AVERAGING RESULT FOR PERIODIC SOLUTIONS OF CARATHEODORY DIFFERENTIAL EQUATIONS. Proceedings of the American Mathematical Society, v. 150, n. 7, p. 10-pg., 2022-07-01. (21/10606-0, 19/10269-3, 18/16430-8)

BUZZI, CLAUDIO; LLIBRE, JAUME; SANTANA, PAULO. Periodic orbits of a Hamiltonian system related with the Friedmann-Robertson-Walker system in rotating coordinates. PHYSICA D-NONLINEAR PHENOMENA, v. 413, DEC 2020. (19/10269-3, 19/21446-3, 18/23194-9)

CARVALHO, TIAGO; GONCALVES, LUIZ FERNANDO; LLIBRE, JAUME. Limit Cycles on Piecewise Smooth Vector Fields with Coupled Rigid Centers. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 31, n. 15, DEC 15 2021. (19/10269-3)

GOUVEIA, MARCIO; OLER, JULIANO G.. Phase Transitions for One-Dimensional Lorenz-Like Expanding Maps. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 53, n. 4, p. 24-pg., 2022-08-25. (19/10269-3)

ANTUNES, ANDRE DO AMARAL; BUGEAUD, YANN; PIRES, BENITO. Switched Server Systems Whose Parameters are Normal Numbers in Base 4. Qualitative Theory of Dynamical Systems, v. 21, n. 4, p. 13-pg., 2022-12-01. (19/10269-3)

NOVAES, DOUGLAS D.. On the Hilbert number for piecewise linear vector fields with algebraic discontinuity set. PHYSICA D-NONLINEAR PHENOMENA, v. 441, p. 15-pg., 2022-12-01. (19/10269-3, 18/13481-0, 21/10606-0)

NOVAES, DOUGLAS D.; RONDON, GABRIEL. On limit cycles in regularized Filippov systems bifurcating from homoclinic-like connections to regular-tangential singularities. PHYSICA D-NONLINEAR PHENOMENA, v. 442, p. 15-pg., 2022-10-01. (19/10269-3, 20/06708-9, 18/13481-0)

PIRES, BENITO. A CHAOTIC DISCRETE-TIME CONTINUOUS-STATE HOPFIELD NETWORK WITH PIECEWISE-AFFINE ACTIVATION FUNCTIONS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, v. N/A, p. 9-pg., 2023-02-23. (19/10269-3)

NOVAES, DOUGLAS D.; PEREIRA, PEDRO C. C. R.. Invariant tori via higher order averaging method: existence, regularity, convergence, stability, and dynamics. MATHEMATISCHE ANNALEN, v. N/A, p. 48-pg., 2023-06-24. (19/10269-3, 18/13481-0, 20/14232-4, 22/09633-5)

CARMONA, VICTORIANO; FERNANDEZ-SANCHEZ, FERNANDO; GARCIA-MEDINA, ELISABETH; NOVAES, DOUGLAS D.. Properties of Poincare half-maps for planar linear systems and some direct applications to periodic orbits of piecewise systems. Electronic Journal of Qualitative Theory of Differential Equations, v. N/A, n. 22, p. 18-pg., 2023-01-01. (19/10269-3, 21/10606-0, 18/13481-0, 22/09633-5)

CIRILO, PATRICIA. ERGODICITY FOR HIGHER DIMENSION CYLINDRICAL CASCADES. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v. 44, n. 4, p. 14-pg., 2023-11-23. (13/16553-9, 19/09045-3, 19/10269-3)

BASTOS, JEFFERSON; BUZZI, CLAUDIO; SANTANA, PAULO. On structural stability of evolutionary stable strategies. Journal of Differential Equations, v. 389, p. 38-pg., 2024-01-24. (21/01799-9, 19/10269-3)

CARVALHO, TIAGO; NOVAES, DOUGLAS D.; TONON, DURVAL J.. Sliding Mode on Tangential Sets of Filippov Systems. JOURNAL OF NONLINEAR SCIENCE, v. 34, n. 4, p. 18-pg., 2024-08-01. (21/12395-6, 18/13481-0, 19/10269-3, 22/02819-6, 22/09633-5)

BASTOS, JEFFERSON L. R.; BUZZI, CLAUDIO A.; TORREGROSA, JOAN. Cyclicity Near Infinity in Piecewise Linear Vector Fields Having a Nonregular Switching Line. Qualitative Theory of Dynamical Systems, v. 22, n. 4, p. 11-pg., 2023-12-01. (19/10269-3)

SANTANA, PAULO. Stability and Cyclicity of Polycycles in Non-smooth Planar Vector Fields. Qualitative Theory of Dynamical Systems, v. 22, n. 4, p. 33-pg., 2023-12-01. (19/10269-3, 21/01799-9)

CUNHA, MATHEUS G. C.; NOVAES, DOUGLAS D.; PONCE, GABRIEL. On the Hausdorff dimension and Cantor set structure of sliding Shilnikov invariant sets. Nonlinearity, v. 37, n. 12, p. 22-pg., 2024-12-02. (18/13481-0, 22/07762-2, 19/10269-3, 22/09633-5)

PESSOA, CLAUDIO; QUEIROZ, LUCAS. Nilpotent centers from analytical systems on center manifolds. Journal of Mathematical Analysis and Applications, v. 525, n. 1, p. 17-pg., 2023-03-02. (19/10269-3, 19/13040-7)

ANTUNES, ANDRE AMARAL; CARVALHO, TIAGO; VARAO, REGIS. On topological entropy of piecewise smooth vector fields. Journal of Differential Equations, v. 362, p. 22-pg., 2023-03-13. (19/10450-0, 16/22475-9, 19/10269-3, 21/12395-6, 17/18255-6, 17/06463-3)

MESSIAS, MARCELO; CANDIDO, MURILO R.. Analytical results on the existence of periodic orbits and canard-type invariant torus in a simple dissipative oscillator. CHAOS SOLITONS & FRACTALS, v. 182, p. 12-pg., 2024-04-11. (23/06076-0, 19/10269-3)

CARMONA, VICTORIANO; FERNANDEZ-SANCHEZ, FERNANDO; NOVAES, DOUGLAS D.. Uniform upper bound for the number of limit cycles of planar piecewise linear differential systems with two zones separated by a straight line. Applied Mathematics Letters, v. 137, p. 8-pg., 2023-03-01. (19/10269-3, 21/10606-0, 18/13481-0, 22/09633-5)

BUZZI, CLAUDIO A.; RODERO, ANA LIVIA; TORREGROSA, JOAN. 3-dimensional piecewise linear and quadratic vector fields with invariant spheres. Electronic Journal of Qualitative Theory of Differential Equations, v. N/A, n. 43, p. 27-pg., 2024-01-01. (19/00440-7, 17/08779-8, 21/12630-5, 19/10269-3)

NOVAES, DOUGLAS D.; PEREIRA, PEDRO C. C. R.. On the periodic and antiperiodic aspects of the Floquet normal form. BULLETIN DES SCIENCES MATHEMATIQUES, v. 190, p. 13-pg., 2023-12-19. (20/14232-4, 18/13481-0, 19/10269-3, 22/09633-5)

CARVALHO, TIAGO. Planar quartic-quadratic fold-fold singularity of Filippov systems and its bifurcation. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 134, p. 31-pg., 2024-04-17. (21/12395-6, 22/02819-6, 19/10269-3)

BELATTAR, MERYEM; CHEURFA, RACHID; BENDJEDDOU, AHMED; SANTANA, PAULO. A class of nonlinear oscillators with non-autonomous first integrals and algebraic limit cycles. Electronic Journal of Qualitative Theory of Differential Equations, v. N/A, n. 50, p. 13-pg., 2023-01-01. (21/01799-9, 19/10269-3)

CARVALHO, TIAGO; CUNHA, JACKSON; EUZEBIO, RODRIGO; FLORENTINO, MARCO. Dynamics of an intermittent HIV treatment using piecewise smooth vector fields with two switching manifolds. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, v. 82, p. 6-pg., 2025-04-01. (21/12395-6, 22/02819-6, 19/10450-0, 19/10269-3)

GASULL, ARMENGOL; RONDON, GABRIEL; DA SILVA, PAULO RICARDO. On the Number of Limit Cycles for Piecewise Polynomial Holomorphic Systems\ast. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, v. 23, n. 3, p. 30-pg., 2024-01-01. (20/06708-9, 22/12123-9, 23/02959-5, 19/10269-3)

MESSIAS, MARCELO; APARECIDO VERRI, JULIANO. Birth and death of a limit cycle through Hopf bifurcations in a model of HIV infection with RT treatment. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, v. N/A, p. 16-pg., 2024-09-25. (19/10269-3)

BASTOS, JEFFERSON L. R.; CAPRIO, DANILO A.; MESSAOUDI, ALI. Shadowing and stability in p-adic dynamics. Journal of Mathematical Analysis and Applications, v. 500, n. 2, p. 28-pg., 2021-03-15. (19/10269-3, 13/24541-0, 15/26161-6)

NOVAES, DOUGLAS D.; SILVA, FRANCISCO B.. HIGHER ORDER ANALYSIS ON THE EXISTENCE OF PERIODIC SOLUTIONS IN CONTINUOUS DIFFERENTIAL EQUATIONS VIA DEGREE THEORY. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, v. 53, n. 2, p. 15-pg., 2021-01-01. (19/10269-3, 18/22689-4, 18/16430-8, 18/13481-0)

DA SILVA, PAULO R.; DE MORAES, JAIME R.. Piecewise-Smooth Slow-Fast Systems. JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, v. 27, n. 1, MAR 2020. (19/10269-3)

MESSIAS, MARCELO; REINOL, ALISSON C.. Periodic Orbits in the Muthuswamy-Chua Simplest Chaotic Circuit. JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, v. N/A, p. 12-pg., 2022-08-15. (19/10269-3)

GOUVEIA, LUIZ F. S.; DA SILVA, PAULO R. R.; RONDON, GABRIEL. Global Phase Portrait and Local Integrability of Holomorphic Systems. Qualitative Theory of Dynamical Systems, v. 22, n. 1, p. 26-pg., 2023-03-01. (20/06708-9, 19/10269-3, 20/04717-0)

ANDRADE, KAMILA DA S.; CESPEDES, OSCAR A. R.; CRUZ, DAYANE R.; NOVAES, DOUGLAS D.. Higher order Melnikov analysis for planar piecewise linear vector fields with nonlinear switching curve. Journal of Differential Equations, v. 287, p. 36-pg., 2021-03-29. (19/10269-3)

PEREIRA, PEDRO C. C. R.; NOVAES, DOUGLAS D.; CANDIDO, MURILO R.. A mechanism for detecting normally hyperbolic invariant tori in differential equations. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, v. 177, p. 45-pg., 2023-09-01. (19/05657-4, 22/09633-5, 18/07344-0, 19/10269-3, 21/10606-0, 20/14232-4, 18/13481-0)

NOVAES, DOUGLAS D.; SILVA, LEANDRO A.. Lyapunov coefficients for monodromic tangential singularities in Filippov vector fields. Journal of Differential Equations, v. 300, p. 565-596, NOV 5 2021. (19/10269-3, 18/13481-0, 18/16430-8)

BUZZI, CLAUDIO A.; RODERO, ANA LIVIA; TORREGROSA, JOAN. Centers and Limit Cycles of Vector Fields Defined on Invariant Spheres. JOURNAL OF NONLINEAR SCIENCE, v. 31, n. 6, DEC 2021. (17/08779-8, 19/10269-3, 19/00440-7)

LLIBRE, JAUME; MESSIAS, MARCELO; REINOL, ALISSON C.. Global Dynamics and Bifurcation of Periodic Orbits in a Modified Nose-Hoover Oscillator. JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, v. 27, n. 3, JUN 2020. (19/10269-3)

GASULL, ARMENGOL; SANTANA, PAULO. On a variant of Hilbert's 16th problem. Nonlinearity, v. 37, n. 12, p. 15-pg., 2024-12-02. (22/14353-1, 21/01799-9, 19/10269-3)

BUZZI, CLAUDIO A.; EUZEBIO, RODRIGO D.; MEREU, ANA C.. Bifurcation of Piecewise Smooth Manifolds from 3D Center-Type Vector Fields. Qualitative Theory of Dynamical Systems, v. 22, n. 4, p. 15-pg., 2023-12-01. (19/10269-3, 18/13481-0)

BRAGA, DENIS DE CARVALHO; DA FONSECA, ALEXANDER FERNANDES; MELLO, LUIS FERNANDO; RIBEIRO, RONISIO MOISES; PESSOA, CLAUDIO GOMES. Crossing Limit Cycles Bifurcating from Two or Three Period Annuli in Discontinuous Planar Piecewise Linear Hamiltonian Differential Systems with Three Zones. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 33, n. 10, p. 17-pg., 2023-08-01. (19/10269-3, 19/07316-0, 23/04061-6)