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Minimal sets of piecewise differential systems in dimension 3

Grant number: 14/18508-3
Support type:Scholarships abroad - Research Internship - Post-doctor
Effective date (Start): January 01, 2015
Effective date (End): June 29, 2015
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Marco Antônio Teixeira
Grantee:Rodrigo Donizete Euzébio
Supervisor abroad: Jaume Llibre
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Research place: Universitat Autònoma de Barcelona (UAB), Spain  
Associated to the scholarship:13/25828-1 - Minimal sets and invariant manifolds in piecewise smooth systems, BP.PD

Abstract

In this project we aim to study the existence and configuration of minimal sets in 3-dimensional piecewise smooth differential systems for two special classes of systems. Our main goal is to investigate the existence of codimension one manifolds filled up (or not) by periodic orbits after a non-smooth perturbation of a continuum of periodic orbits. Codimension two manifolds (limit cycles) will be also investigated. The methods involve geometric manipulation of the respective manifolds and eventually non-smooth versions of methods based on the Malkin's bifurcation funcion. (AU)

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Scientific publications (4)
(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)
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)
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)
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)
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)

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