Differential equations: reversibility and bifurcations

Author(s)

Ricardo Miranda Martins

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2011-02-28

Examining board members

Marco Antonio Teixeira; Eduardo Garibaldi; Clodoaldo Grotta Ragazzo; Daniel Smania Brandão; Ronaldo Alves Garcia

• Advisor: Marco Antonio Teixeira

Abstract

In the first part of this thesis, we study the similarity between reversible and Hamiltonian dynamical systems, from a formal viewpoint. We restrict ourselves to systems defined around an isolated and symmetric equilibria. We show that, under some conditions, such systems are formally orbitally equivalent to Hamiltonian vector fields. In the second part, we study the existence of minimal sets for some families of diferential equations. We obtain conditions for the existence of the invariant cylinders and tori for perturbed reversible systems. (AU)

• FAPESP's process: 07/05215-4 - The Hamiltonian structure of normal forms for elliptic equilibria of reversible vector fields in 4D and 6D
• Grantee: Ricardo Miranda Martins
• Support Opportunities: Scholarships in Brazil - Doctorate