Analytic Conjugacy Between Reversible and Hamiltonian Systems in the Plane
DOI:
https://doi.org/10.21167/cqdv27e27009Keywords:
reversible systems; hamiltonian systems; normal forms; analytic conjugacy.Abstract
We study the local structure of analytic planar vector fields that are reversible
with respect to the linear involution \(R(u,v)=(u,-v)\). We show that every such
reversible system with a nondegenerate equilibrium is locally analytically
conjugate to a Hamiltonian vector field. We provide explicit Hamiltonian normal
forms for the elliptic and hyperbolic cases, and we prove that the conjugacy can be chosen equivariantly with respect to the involution. We also discuss known obstructions to global equivalence and briefly comment on the situation in higher dimensions.
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