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Minimal sets and invariant manifolds in piecewise smooth systems

Grant number: 13/25828-1
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): July 01, 2014
Effective date (End): February 11, 2016
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Marco Antônio Teixeira
Grantee:Rodrigo Donizete Euzébio
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated research grant:12/18780-0 - Geometry of control systems, dynamical and stochastics systems, AP.TEM
Associated scholarship(s):14/18508-3 - Minimal sets of piecewise differential systems in dimension 3, BE.EP.PD

Abstract

In this project we propose to investigate the existence of typical minimal sets and invariant manifolds in piecewise smooth systems. In particular, we are interested in the bifurcation of limit cycles through a piecewise smooth perturbation of manifolds filled by periodic orbits such as a band of bi-dimensional manifolds and the permanence of such objects. The methods used to approach the proposed problems are based in the averaging theory, the regularization of piecewise smooth vectors fields and a variation of the Melnikov method for piecewise smooth systems.

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Scientific publications (8)
(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.; CARVALHO, TIAGO; EUZEBIO, RODRIGO D.. ON POINCARE BENDIXSON THEOREM AND NON-TRIVIAL MINIMAL SETS IN PLANAR NONSMOOTH VECTOR FIELDS. PUBLICACIONS MATEMATIQUES, v. 62, n. 1, p. 113-131, . (13/25828-1, 13/24541-0, 14/02134-7, 14/18508-3)
CARVALHO, TIAGO; EUZEBIO, RODRIGO D.; TEIXEIRA, MARCO ANTONTO; TONON, DURVAL JOSE. Birth of limit cycles from a 3D triangular center of a piecewise smooth vector field. IMA JOURNAL OF APPLIED MATHEMATICS, v. 82, n. 3, p. 561-578, . (14/18508-3, 13/25828-1, 14/02134-7)
EUZEBIO, RODRIGO D.; LLIBRE, JAUME. Sufficient conditions for the existence of periodic solutions of the extended Duffing-Van der Pol oscillator. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, v. 93, n. 8, p. 1358-1382, . (13/25828-1, 12/05635-1, 10/18015-6)
EUZEBIO, RODRIGO D.; LLIBRE, JAUME. Zero-Hopf bifurcation in a Chua system. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, v. 37, p. 31-40, . (13/25828-1, 12/05635-1, 10/18015-6)
BUZZI, C. A.; EUZEBIO, R. D.; MEREU, A. C.. Bifurcation of limit cycles from a non-smooth perturbation of a two-dimensional isochronous cylinder. BULLETIN DES SCIENCES MATHEMATIQUES, v. 140, n. 5, p. 519-540, . (14/18508-3, 12/18780-0, 13/24541-0, 13/25828-1)
EUZEBIO, RODRIGO; PAZIM, RUBENS; PONCE, ENRIQUE. Jump bifurcations in some degenerate planar piecewise linear differential systems with three zones. PHYSICA D-NONLINEAR PHENOMENA, v. 325, p. 74-85, . (13/25828-1, 14/18508-3)
DE CARVALHO, TIAGO; EUZEBIO, RODRIGO DONIZETE; LLIBRE, JAUME; TONON, DURVAL JOSE. DETECTING PERIODIC ORBITS IN SOME 3D CHAOTIC QUADRATIC POLYNOMIAL DIFFERENTIAL SYSTEMS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, v. 21, n. 1, p. 1-11, . (13/25828-1, 14/02134-7)
EUZEBIO, RODRIGO D.; GOUVEIA, MARCIO R. A.. Poincare recurrence theorem for non-smooth vector fields. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, v. 68, n. 2, . (13/24541-0, 13/25828-1)

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