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Persistence of Periodic Orbits for Perturbed Dissipative Dynamical Systems

  • Jack K. Hale
  • Geneviève Raugel
Chapter
Part of the Fields Institute Communications book series (FIC, volume 64)

Abstract

This paper is devoted to the study of the persistence of periodic solutions under perturbations in dynamical systems generated by evolutionary equations, which are not smoothing in finite time, but only asymptotically smoothing. Assuming that the periodic solution of the unperturbed system is non-degenerate, we want to prove the existence and uniqueness of a periodic solution for the perturbed equation in the neighbourhood of the unperturbed solution (with a period near the period of the periodic solution of the unperturbed problem). We review some methods of proofs, used in the case of systems of ordinary differential equations, and discuss their extensions to the infinite-dimensional case.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Center for Dynamical Systems and Nonlinear Studies, School of MathematicsGeorgia Institute of TechnologyAtlantaUSA
  2. 2.CNRS, Laboratoire de Mathématiques d’OrsayUniv Paris-SudOrsay CedexFrance

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