Characterizing Orbital-Reversibility Through Normal Forms

  1. Algaba, A. 1
  2. Checa, I. 1
  3. Gamero, E. 2
  4. García 1
  1. 1 Universidad de Huelva
    info

    Universidad de Huelva

    Huelva, España

    ROR https://ror.org/03a1kt624

  2. 2 Universidad de Sevilla
    info

    Universidad de Sevilla

    Sevilla, España

    ROR https://ror.org/03yxnpp24

Revista:
Qualitative theory of dynamical systems

ISSN: 1575-5460

Año de publicación: 2021

Volumen: 20

Número: 2

Tipo: Artículo

DOI: 10.1007/S12346-021-00478-6 DIALNET GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Qualitative theory of dynamical systems

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.

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