Minimal sets of piecewise differential systems in dimension 3

• Grant number: 14/18508-3
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: January 01, 2015
• End date: June 29, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Marco Antônio Teixeira
• Grantee: Rodrigo Donizete Euzébio
• Supervisor: Jaume Llibre
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: 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)

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)

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, 2018. (13/24541-0, 14/18508-3, 13/25828-1, 14/02134-7)

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, JUN 2017. (14/18508-3, 13/25828-1, 14/02134-7)

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, JUN 15 2016. (14/18508-3, 13/25828-1)

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, JUN 2016. (14/18508-3, 12/18780-0, 13/24541-0, 13/25828-1)