Perturbations of reversible systems

Author(s)

Ana Cristina de Oliveira Mereu

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2009-05-29

Examining board members

Marco Antonio Teixeira; Eduardo Garibaldi; Claudio Aguinaldo Buzzi; Ronaldo Alves Garcia; Luis Fernando de Osorio Mello

• Advisor: Marco Antonio Teixeira

Abstract

In this work we study the existence and persistence of some minimal sets in perturbations of reversible systems. First we make non reversible perturbations of centers in R2 and R4 and we detect conditions for the existence of limit cycles and invariant tori. We study the existence of periodic solutions of the perturbations of a family of di_erential equations expressed by x(2n) + a (2n-2)/2 +¿+ a1x(2) + x = 0 ; for n = 2; 3. The existence and persistence of homoclinic orbits in such equations are also discussed. (AU)