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A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: Rigorous results
- Source :
-
Journal of Differential Equations . Sep2006, Vol. 228 Issue 2, p530-579. 50p. - Publication Year :
- 2006
-
Abstract
- Abstract: In this paper we prove rigorous results on persistence of invariant tori and their whiskers. The proofs are based on the parameterization method of [X. Cabré, E. Fontich, R. de la Llave, The parameterization method for invariant manifolds. I. Manifolds associated to non-resonant subspaces, Indiana Univ. Math. J. 52 (2) (2003) 283–328; X. Cabré, E. Fontich, R. de la Llave, The parameterization method for invariant manifolds. II. Regularity with respect to parameters, Indiana Univ. Math. J. 52 (2) (2003) 329–360]. The invariant manifolds results proved here include as particular cases of the usual (strong) stable and (strong) unstable manifolds, but also include other non-resonant manifolds. The method lends itself to numerical implementations whose analysis and implementation is studied in [A. Haro, R. de la Llave, A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: Numerical algorithms, preprint, 2005; A. Haro, R. de la Llave, A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: Numerical implementation and examples, preprint, 2005]. The results are stated as a posteriori results. Namely, that if one has an approximate solution which is not degenerate, then, one has a true solution not too far from the approximate one. This can be used to validate the results of numerical computations. [Copyright &y& Elsevier]
- Subjects :
- *MATHEMATICS
*INVARIANT subspaces
*FUNCTIONAL analysis
*ALGORITHMS
Subjects
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 228
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 21913267
- Full Text :
- https://doi.org/10.1016/j.jde.2005.10.005