# American Institute of Mathematical Sciences

September  2011, 31(3): 763-777. doi: 10.3934/dcds.2011.31.763

## On the birth of minimal sets for perturbed reversible vector fields

 1 Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia 2 Instituto de Matemática, Estatística e Computação Cientíﬁca, Universidade Estadual de Campinas, 13083–859 Campinas, SP, Brazil, Brazil

Received  June 2010 Revised  May 2011 Published  August 2011

The results in this paper fit into a program to study the existence of periodic orbits, invariant cylinders and tori filled with periodic orbits in perturbed reversible systems. Here we focus on bifurcations of one-parameter families of periodic orbits for reversible vector fields in $\mathbb{R}^4$. The main used tools are normal forms theory, Lyapunov-Schmidt method and averaging theory.
Citation: Jaume Llibre, Ricardo Miranda Martins, Marco Antonio Teixeira. On the birth of minimal sets for perturbed reversible vector fields. Discrete & Continuous Dynamical Systems, 2011, 31 (3) : 763-777. doi: 10.3934/dcds.2011.31.763
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