Characterizing Orbital-Reversibility Through Normal Forms

  1. Antonio Algaba Durán 1
  2. Isabel Checa Camacho 1
  3. Estanislao Gamero Gutiérrez 2
  4. Cristóbal García García 1
  1. 1 Universidad de Huelva

    Universidad de Huelva

    Huelva, España


  2. 2 Universidad de Sevilla

    Universidad de Sevilla

    Sevilla, España


Qualitative theory of dynamical systems

ISSN: 1575-5460

Year of publication: 2021

Volume: 20

Issue: 2

Type: Article

DOI: 10.1007/S12346-021-00478-6 DIALNET GOOGLE SCHOLAR lock_openOpen access editor

More publications in: Qualitative theory of dynamical systems


Cited by

  • Scopus Cited by: 2 (18-11-2023)
  • Web of Science Cited by: 2 (22-10-2023)
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  • Year 2021
  • Journal Impact Factor: 0.931
  • Journal Impact Factor without self cites: 0.763
  • Article influence score: 0.314
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  • Area: Discrete Mathematics and Combinatorics Percentile: 70
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(Data updated as of 06-03-2023)
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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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