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On Some Reversible Cubic Systems

Author

Listed:
  • Barbara Arcet

    (Center for Applied Mathematics and Theoretical Physics, University of Maribor, 2000 Maribor, Slovenia
    These authors contributed equally to this work.)

  • Valery G. Romanovski

    (Center for Applied Mathematics and Theoretical Physics, University of Maribor, 2000 Maribor, Slovenia
    Faculty of Electrical Engineering and Computer Science, University of Maribor, 2000 Maribor, Slovenia
    Faculty of Natural Science and Mathematics, University of Maribor, 2000 Maribor, Slovenia
    These authors contributed equally to this work.)

Abstract

We study three systems from the classification of cubic reversible systems given by Żoła̧dek in 1994. Using affine transformations and elimination algorithms from these three families the six components of the center variety are derived and limit-cycle bifurcations in neighborhoods of the components are investigated. The invariance of the systems with respect to the generalized involutions introduced by Bastos, Buzzi and Torregrosa in 2021 is discussed. Computations are performed using the computer algebra systems Mathematica and Singular .

Suggested Citation

  • Barbara Arcet & Valery G. Romanovski, 2021. "On Some Reversible Cubic Systems," Mathematics, MDPI, vol. 9(12), pages 1-20, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1446-:d:578838
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    Cited by:

    1. Lijun Wei & Yun Tian & Yancong Xu, 2022. "The Number of Limit Cycles Bifurcating from an Elementary Centre of Hamiltonian Differential Systems," Mathematics, MDPI, vol. 10(9), pages 1-14, April.

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