Period function for a class of Hamiltonian systems

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Abstract

This paper studies the period function of the class of Hamiltonian systems x=-Hy, y=Hx where H(x, y) has the special form H(x, y)=F(x)+G(y) and the origin is a non-degenerate center. More concretely, if T(h) denotes the period of the periodic orbit contained in H(x, y)=h we solve the inverse problem of characterizing all systems with a given function T(h). We also characterize the limiting behaviour of T at infinity when the origin is a global center and apply this result to prove, among other results, that there are no nonlinear polynomial isochronous centers in this family. © 2000 Academic Press.
Original languageEnglish
Pages (from-to)180-199
JournalJournal of Differential Equations
Volume168
DOIs
Publication statusPublished - 20 Nov 2000

Keywords

  • Hamiltonian system
  • Inverse problem
  • Isochronicity
  • Period function

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