Regularization and minimal sets for non-smooth dynamical systems

• Grant number: 12/10231-7
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: September 01, 2012
• End date: July 31, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Marco Antônio Teixeira
• Grantee: Douglas Duarte Novaes
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 07/06896-5 - Geometry of control, dynamical and stochastic systems, AP.TEM
• Associated scholarship(s): 13/16492-0 - Averaging Theory for studying the periodic solutions of the differential systems and its applications, BE.EP.DR

Abstract

The purpose of this project is to present some aspects of thegeometric theory of a class of non-smooth dynamical systems named Filippov Systems.Our main concern is to establish conditions for the existence of typicalminimal sets that often appear in many applications. The main toolsinvolve a combination of the regularization method and classical Averaging Theory.

Scientific publications

(5)

(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)

LLIBRE, JAUME; MEREU, ANA C.; NOVAES, DOUGLAS D.. Averaging theory for discontinuous piecewise differential systems. Journal of Differential Equations, v. 258, n. 11, p. 4007-4032, JUN 5 2015. (12/18780-0, 12/10231-7)

NOVAES, DOUGLAS D.; JEFFREY, MIKE R.. Regularization of hidden dynamics in piecewise smooth flows. Journal of Differential Equations, v. 259, n. 9, p. 4615-4633, NOV 5 2015. (12/10231-7)

GOUVEIA, MARCIO R. A.; LLIBRE, JAUME; NOVAES, DOUGLAS D.. On limit cycles bifurcating from the infinity in discontinuous piecewise linear differential systems. Applied Mathematics and Computation, v. 271, p. 365-374, NOV 15 2015. (13/13344-0, 12/10231-7)

LLIBRE, JAUME; NOVAES, DOUGLAS D.; TEIXEIRA, MARCO A.. Maximum number of limit cycles for certain piecewise linear dynamical systems. NONLINEAR DYNAMICS, v. 82, n. 3, p. 1159-1175, NOV 2015. (12/18780-0, 12/10231-7)

DOUGLAS D. NOVAES. Perturbações do pêndulo amortecido: encontrando soluções periódicas via método averaging. Revista Brasileira de Ensino de Física, v. 35, n. 1, p. 01-07, 2013-03-00. (12/10231-7)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

NOVAES, Douglas Duarte. Regularização e conjuntos minimais para sistemas dinâmicos não suaves. 2015. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.