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Persistence of Periodic Orbits for Perturbed Dissipative Dynamical Systems

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Infinite Dimensional Dynamical Systems

Part of the book series: Fields Institute Communications ((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.

Mathematics Subject Classification 2010(2010): Primary 35B10, 35B25, 37L50, 37L05 Secondary 35Q30, 35Q35

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Author information

Authors and Affiliations

  1. Center for Dynamical Systems and Nonlinear Studies, School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Jack K. Hale

  2. CNRS, Laboratoire de Mathématiques d’Orsay, Univ Paris-Sud, Orsay Cedex, F-91405, France

    Geneviève Raugel

Authors
  1. Jack K. Hale
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  2. Geneviève Raugel
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Correspondence to Geneviève Raugel .

Editor information

Editors and Affiliations

  1. Division of Applied Mathematics, Brown University, Providence, RI, USA

    John Mallet-Paret

  2. Department of Mathematics and Statistics, York University, Toronto, ON, Canada

    Jianhong Wu  & Huaiping Zhu  & 

  3. Georgia Institute of Technology, School of Mathematics, Atlanta, GA, USA

    Yingfei Yi

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Hale, J.K., Raugel, G. (2013). Persistence of Periodic Orbits for Perturbed Dissipative Dynamical Systems. In: Mallet-Paret, J., Wu, J., Yi, Y., Zhu, H. (eds) Infinite Dimensional Dynamical Systems. Fields Institute Communications, vol 64. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4523-4_1

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