Conjugação analítica entre sistemas reversíveis e hamiltonianos no plano

Abstract

This paper investigates whether planar analytic reversible vector fields in a neighborhood of a nondegenerate equilibrium point can be locally described by analytic Hamiltonian systems. We prove that every planar analytic vector field reversible with re- spect to the linear involution $𝑅(𝑥, 𝑦) = (𝑥, −𝑦)$ and possessing a nondegenerate equilibrium point is locally analytically con- jugate to a planar Hamiltonian system. This result promotes to the analytic setting an equivalence that was previously known only at the formal level.