Ergodic and qualitative theories of dynamical systems II

• Grant number: 19/10269-3
• Support type: Research Projects - Thematic Grants
• Duration: August 01, 2019 - July 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal researcher: Claudio Aguinaldo Buzzi
• Grantee: Claudio Aguinaldo Buzzi
• Home 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
• Assoc. 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 scholarship(s): 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; + associated scholarships 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; 19/20500-4 - Abundance of transitive linear operators in infinite dimension, BP.MS; 19/13040-7 - Nilpotent centers on the center manifolds, BP.DR - 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

(34)

(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)

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. (19/10269-3, 18/13481-0, 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)

DARJI, UDAYAN B.; PIRES, BENITO. CHAOS AND FREQUENT HYPERCYCLICITY FOR COMPOSITION OPERATORS. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, v. 64, n. 3, p. 513-531, AUG 2021. (18/06916-0, 17/19360-8, 19/10269-3)

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)

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)

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)

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)

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)

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)

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)

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)

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)

BERNARDES JR, NILSON C.; MESSAOUDI, ALI. A GENERALIZED GROBMAN-HARTMAN THEOREM. Proceedings of the American Mathematical Society, v. 148, n. 10, p. 4351-4360, OCT 2020. (17/22588-0, 19/10269-3)

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)

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)

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)

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)

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)

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. (19/10269-3, 18/13481-0, 18/16430-8, 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)

BASTOS, JEFFERSON L. R.; BUZZI, CLAUDIO A.; TORREGROSA, JOAN. ORBITALLY SYMMETRIC SYSTEMS WITH APPLICATIONS TO PLANAR CENTERS. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, v. 20, n. 10, p. 3301-3329, OCT 2021. (17/03352-6, 19/10269-3, 13/24541-0)

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, 18/05098-2, 16/00242-2)

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)

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.; 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. (19/10269-3, 18/13481-0, 18/16430-8, 20/06708-9)

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; 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)

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)

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)

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)

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)