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Erschienen in:
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2013 | OriginalPaper | Buchkapitel

Persistence of Periodic Orbits for Perturbed Dissipative Dynamical Systems

verfasst von : Jack K. Hale, Geneviève Raugel

Erschienen in: Infinite Dimensional Dynamical Systems

Verlag: Springer New York

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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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Nächstes Kapitel Spectral Theory for Forward Nonautonomous Parabolic Equations and Applications
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Metadaten
Titel
Persistence of Periodic Orbits for Perturbed Dissipative Dynamical Systems
verfasst von
Jack K. Hale
Geneviève Raugel
Copyright-Jahr
2013
Verlag
Springer New York
Buch
Infinite Dimensional Dynamical Systems

Print ISBN: 978-1-4614-4522-7

Electronic ISBN: 978-1-4614-4523-4

Copyright-Jahr: 2013

DOI
https://doi.org/10.1007/978-1-4614-4523-4_1