A new algorithm for the computation of the Lyapunov constants for some degenerated critical points

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Abstract

The center problem for degenerated monodromic critical points is far to be solved in general. In this paper we give a procedure to solve it for a particular perturbation of critical points which dominant part near the critical point is x2n-1∂/∂x + y2m-1∂/∂y. For these critical points the problem is solved by writing its associated differential equation in the generalized polar coordinates introduced by Lyapunov and by developing a new method of computation of the so called generalized Lyapunov contants. This method is based into the transformation of the differential equation into the perturbation of a Hamiltonian system. Finally, the method is applied to solve the center and the stability problem for a particular family of differential equations.
Original languageEnglish
Pages (from-to)4479-4490
JournalNonlinear Analysis, Theory, Methods and Applications
Volume47
DOIs
Publication statusPublished - 1 Aug 2001

Keywords

  • Center point
  • Generalized Lyapunov constants

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