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Erschienen in:
An Overview of the Parameterization Method for Invariant Manifolds Kapitel lesen Erstes Kapitel lesen

2016 | OriginalPaper | Buchkapitel

3. The Parameterization Method for Quasi-Periodic Systems: From Rigorous Results to Validated Numerics

verfasst von : Jordi-Lluís Figueras, Àlex Haro

Erschienen in: The Parameterization Method for Invariant Manifolds

Verlag: Springer International Publishing

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Abstract

This chapter developes the “from theory-to algorithms-to computations-to validations” program for response tori in quasi-periodically forced systems. First, it provides a full proof of a Kantorovich-like theorem for invariant tori in discrete quasi-periodic systems. The proof of this theorem leads to several algorithms for the computation of invariant tori in this context, that are also detailed. Next, it is explained a computer assisted methodology for the validation of numerical results based on the previous a posteriori theorem. The chapter ends with three examples: validation of saddle invariant tori on the verge of breakdown, computation of a rigorous upper bound of the measure of Cantor-like spectra of a discrete Schrödinger operator, and validation of an attracting torus that by direct double precision seems to be a strange nonchaotic attractor.

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Vorheriges Kapitel Seminumerical Algorithms for Computing Invariant Manifolds of Vector Fields at Fixed Points
Nächstes Kapitel The Parameterization Method in KAM Theory
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Metadaten
Titel
The Parameterization Method for Quasi-Periodic Systems: From Rigorous Results to Validated Numerics
verfasst von
Jordi-Lluís Figueras
Àlex Haro
Copyright-Jahr
2016
Buch
The Parameterization Method for Invariant Manifolds

Print ISBN: 978-3-319-29660-9

Electronic ISBN: 978-3-319-29662-3

Copyright-Jahr: 2016

DOI
https://doi.org/10.1007/978-3-319-29662-3_3

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