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Introduction and examples

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1645)

Abstract

This book investigates the occurrence of quasi-periodic motions in dynamical systems with special emphasis on the persistence of these motions under small perturbations of the system. Quasi-periodic motions densely fill up invariant tori, therefore this study can be regarded as a part of a more general theory of invariant manifolds. The existence, persistence and other properties of invariant manifolds play a fundamental rôle in the analysis of nonlinear dynamical systems [67,115,158,356]. In this book we confine ourselves with finite dimensional systems. For the theory of quasi-periodic motions in infinite dimensional dynamical systems, the reader is recommended to consult, e.g., [185,186,279–281] and references therein.

Keywords

  • Vector Field
  • Invariant Torus
  • Frequency Vector
  • Small Divisor
  • Diophantine Condition

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1996 Springer-Verlag Berlin Heidelberg

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(1996). Introduction and examples. In: Quasi-Periodic Motions in Families of Dynamical Systems. Lecture Notes in Mathematics, vol 1645. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-49613-7_1

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  • DOI: https://doi.org/10.1007/978-3-540-49613-7_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62025-9

  • Online ISBN: 978-3-540-49613-7

  • eBook Packages: Springer Book Archive