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The conjugacy theory

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

Abstract

In this chapter, we present precise formulations of the quasi-periodicity persistence theorems in the dissipative context, volume preserving context, Hamiltonian isotropic context and reversible context 1 (see Sections 1.3–1.4). The parameter μ labeling the vector fields is always assumed to vary in an open domain P ⊂ Rs, s ≥ 0. All the quantities δ j , ε j α j , β j are supposed to be real. The symbols \( \mathcal{O}_d \left( a \right) \) denote a neighborhood of a point a in the Euclidean space Rd [we write \( \mathcal{O}\left( a \right) \) instead of \( \mathcal{O}_1 \left( a \right) \)]. The letter Y denotes an open domain in Rd. Also, RPd is the d-dimensional real projective space (d ∈ Z+) and Π : Rd\ {0} → RPd−1 for d ∈ N denotes the natural projection.

Keywords

  • Vector Field
  • Invariant Torus
  • Analytic Family
  • Hamiltonian Vector Field
  • CONJUGACY Theory

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). The conjugacy theory. 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_2

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  • DOI: https://doi.org/10.1007/978-3-540-49613-7_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62025-9

  • Online ISBN: 978-3-540-49613-7

  • eBook Packages: Springer Book Archive