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
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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
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