On the birth of minimal sets for perturbed reversible vector fields | Zendy

Jaume Llibre | Zendy; Ricardo Miranda Martins | Zendy; Marco Antônio Teixeira | Zendy

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On the birth of minimal sets for perturbed reversible vector fields

Author(s) -

Jaume Llibre,

Ricardo Miranda Martins,

Marco Antônio Teixeira

Publication year - 2011

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2011.31.763

Subject(s) - periodic orbits , torus , invariant (physics) , mathematics , focus (optics) , vector field , kolmogorov–arnold–moser theorem , pure mathematics , dynamical systems theory , lyapunov function , mathematical analysis , physics , mathematical physics , geometry , quantum mechanics , nonlinear system , optics

Agraïments: The second author is partially supported by a FAPESP–BRAZIL grant 2007/05215-4. The third author is partially supported by a FAPESP–BRAZIL grant 2007/06896–5. All the authors are also supported by the joint project CAPES-MECD grant PHB-2009-0025-PThe 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 R4. The main used tools are normal forms theory, Lyapunov-Schmidt method and averaging theory

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