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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
Principal researchers: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
19/13040-7 - 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 (19)
(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)
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. Web of Science Citations: 0.
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. Web of Science Citations: 0.
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. Web of Science Citations: 0.
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. Web of Science Citations: 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. Web of Science Citations: 1.
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. Web of Science Citations: 0.
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. Web of Science Citations: 0.
CANDIDO, MURILO R.; NOVAES, DOUGLAS D.; VALLS, CLAUDIA. Periodic solutions and invariant torus in the Rossler system. Nonlinearity, v. 33, n. 9 SEP 2020. Web of Science Citations: 0.
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. Web of Science Citations: 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. Web of Science Citations: 0.
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. Web of Science Citations: 0.
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. Web of Science Citations: 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. Web of Science Citations: 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. Web of Science Citations: 0.
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. Web of Science Citations: 0.
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. Web of Science Citations: 0.
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. Web of Science Citations: 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. Web of Science Citations: 1.
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. Web of Science Citations: 0.

Please report errors in scientific publications list by writing to: cdi@fapesp.br.