Minimal sets and invariant manifolds in piecewise smooth systems

• Grant number: 13/25828-1
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: July 01, 2014
• End date: February 11, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Marco Antônio Teixeira
• Grantee: Rodrigo Donizete Euzébio
• Host 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.

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)

EUZEBIO, RODRIGO D.; LLIBRE, JAUME. Zero-Hopf bifurcation in a Chua system. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, v. 37, p. 31-40, OCT 2017. (10/18015-6, 13/25828-1, 12/05635-1)

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, 2016. (10/18015-6, 13/25828-1, 12/05635-1)

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)

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, JAN 2016. (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)

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, APR 2017. (13/24541-0, 13/25828-1)