Abstract
In the dissipative context, volume preserving context with p = 2 (hyperbolic case) or p > 2, Hamiltonian isotropic context, and reversible context 1, it is interesting to consider the restrictions of the unperturbed family of vector fields X and perturbed one \( \tilde X \) to the center manifold. Here we have excluded the volume preserving context with p = 1 and p = 2 (elliptic case) since for these cases, the center manifold always coincides with the whole phase space. The center manifold persists under perturbations [67,115,158,356] but becomes, generally speaking, only finitely differentiable [12,347]. However, we can apply the finitely differentiable versions of the “relaxed” Theorems 2.8, 2.9, 2.11, 2.12 to the restrictions of X and \( \tilde X \) to the center manifold, see [151, 243,277,278,306] as well as [62,162].
Keywords
- Invariant Torus
- Frequency Vector
- Imaginary Eigenvalue
- Continuation Theorem
- Nonreal Eigenvalue
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© 1996 Springer-Verlag Berlin Heidelberg
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(1996). The continuation 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_3
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DOI: https://doi.org/10.1007/978-3-540-49613-7_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62025-9
Online ISBN: 978-3-540-49613-7
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