On the number of critical periods for planar polynomial systems

Anna Cima, Armengol Gasull, Paulo R. da Silva

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Abstract

In this paper we get some lower bounds for the number of critical periods of families of centers which are perturbations of the linear one. We give a method which lets us prove that there are planar polynomial centers of degree ℓ with at least 2 [(ℓ - 2) / 2] critical periods as well as study concrete families of potential, reversible and Liénard centers. This last case is studied in more detail and we prove that the number of critical periods obtained with our approach does not increases with the order of the perturbation. © 2007 Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)1889-1903
JournalNonlinear Analysis, Theory, Methods and Applications
Volume69
DOIs
Publication statusPublished - 1 Oct 2008

Keywords

  • Critical periods
  • Hamiltonian centers
  • Liénard centers
  • Period function
  • Perturbations
  • Potential systems
  • Reversible centers

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    Cima, A., Gasull, A., & da Silva, P. R. (2008). On the number of critical periods for planar polynomial systems. Nonlinear Analysis, Theory, Methods and Applications, 69, 1889-1903. https://doi.org/10.1016/j.na.2007.07.031