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Orbital Reversibility of Planar Vector Fields

Author

Listed:
  • Antonio Algaba

    (Centro de Estudios Avanzados en Física, Departament Ciencias Integradas, Matemáticas y Computación, Facultad de Ciencias, University of Huelva, 21007 Huelva, Spain)

  • Cristóbal García

    (Centro de Estudios Avanzados en Física, Departament Ciencias Integradas, Matemáticas y Computación, Facultad de Ciencias, University of Huelva, 21007 Huelva, Spain)

  • Jaume Giné

    (Inspires Research Centre, Departament de Matemàtica, Universitat de Lleida, Av. Jaume II, 69, 25001 Lleida, Spain)

Abstract

In this work we use the normal form theory to establish an algorithm to determine if a planar vector field is orbitally reversible. In previous works only algorithms to determine the reversibility and conjugate reversibility have been given. The procedure is useful in the center problem because any nondegenerate and nilpotent center is orbitally reversible. Moreover, using this algorithm is possible to find degenerate centers which are orbitally reversible.

Suggested Citation

  • Antonio Algaba & Cristóbal García & Jaume Giné, 2020. "Orbital Reversibility of Planar Vector Fields," Mathematics, MDPI, vol. 9(1), pages 1-25, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2020:i:1:p:14-:d:466861
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    References listed on IDEAS

    as
    1. Han, Maoan & Petek, Tatjana & Romanovski, Valery G., 2018. "Reversibility in polynomial systems of ODE’s," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 55-71.
    2. Lamb, J.S.W. & Roberts, J.A.G. & Capel, H.W., 1993. "Conditions for local (reversing) symmetries in dynamical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 197(3), pages 379-422.
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    1. Lamb, Jeroen S.W., 1996. "Area-preserving dynamics that is not reversible," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 228(1), pages 344-365.

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