CPAA
Formal equivalence between normal forms of reversible and hamiltonian dynamical systems
Ricardo Miranda Martins
Communications on Pure & Applied Analysis 2014, 13(2): 703-713 doi: 10.3934/cpaa.2014.13.703
We show the existence of formal equivalences between $2n$-dimensional reversible and Hamiltonian vector fields. The main tool we employ is the normal form theory.
keywords: normal forms. Hamiltonian systems Reversible vector fields
CPAA
On the similarity of Hamiltonian and reversible vector fields in 4D
Ricardo Miranda Martins Marco Antonio Teixeira
Communications on Pure & Applied Analysis 2011, 10(4): 1257-1266 doi: 10.3934/cpaa.2011.10.1257
We study the existence of formal conjugacies between reversible vector fields and Hamiltonian vector fields in 4D around a generic singularity. We construct conjugacies for a generic class of reversible vector fields. We also show that reversible vector fields are formally orbitally equivalent to polynomial decoupled Hamiltonian vector fields. The main tool we employ is the normal form theory.
keywords: reversible vector field Hamiltonian vector field. Normal form
DCDS
On the birth of minimal sets for perturbed reversible vector fields
Jaume Llibre Ricardo Miranda Martins Marco Antonio Teixeira
Discrete & Continuous Dynamical Systems - A 2011, 31(3): 763-777 doi: 10.3934/dcds.2011.31.763
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.
keywords: Invariant torus Limit cycle Averaging method Isochronous center Reversible system. Periodic orbit

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