(2026-07-08) Nacimento, Francisco José dos Santos; https://orcid.org/0009-0004-9536-7979; http://lattes.cnpq.br/9091581147583991
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.
