Characterizing Orbital-Reversibility Through Normal Forms

• Algaba, A. ^[1] ; Checa, I. ^[1] ; Gamero, E. ^[2] ; García ^[1]
  1. [1] Universidad de Huelva

     Universidad de Huelva

     Huelva, España

     
  2. [2] Universidad de Sevilla

     Universidad de Sevilla

     Sevilla, España

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 20, Nº 2, 2021
• Idioma: inglés
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• Resumen

  • In this paper, we consider the orbital-reversibility problem for an n-dimensional vector field, which consists in determining if there exists a time-reparametrization that transforms the vector field into a reversible one. We obtain an orbital normal form that brings out the invariants that prevent the orbital-reversibility. Hence, we obtain a necessary condition for a vector field to be orbital-reversible. Namely, the existence of an orbital normal form which is reversible to the change of sign in some of the state variables. The necessary condition provides an algorithm, based on the vanishing of the orbital normal form terms that avoid the orbital-reversibility, that is applied to some families of planar and three-dimensional systems.