The parameterization method for invariant manifolds [electronic resource] : from rigorous results to effective computations / Álex Haro, Marta Canadell, Jordi-Lluis Figueras, Alejandro Luque, Josep Maria Mondelo.
2016
QA613
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Title
The parameterization method for invariant manifolds [electronic resource] : from rigorous results to effective computations / Álex Haro, Marta Canadell, Jordi-Lluis Figueras, Alejandro Luque, Josep Maria Mondelo.
ISBN
9783319296623 (electronic book)
3319296620 (electronic book)
9783319296609
3319296620 (electronic book)
9783319296609
Published
Switzerland : Springer, 2016.
Language
English
Description
1 online resource (xvi, 267 pages) : illustrations.
Item Number
10.1007/978-3-319-29662-3 doi
Call Number
QA613
Dewey Decimal Classification
515/.39
Summary
This monograph presents some theoretical and computational aspects of the parameterization method for invariant manifolds, focusing on the following contexts: invariant manifolds associated with fixed points, invariant tori in quasi-periodically forced systems, invariant tori in Hamiltonian systems and normally hyperbolic invariant manifolds. This book provides algorithms of computation and some practical details of their implementation. The methodology is illustrated with 12 detailed examples, many of them well known in the literature of numerical computation in dynamical systems. A public version of the software used for some of the examples is available online. The book is aimed at mathematicians, scientists and engineers interested in the theory and applications of computational dynamical systems.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed April 26, 2016).
Added Author
Haro, A. (Alex), 1969- author.
Canadell, Marta, author.
Figueras, Jordi-Lluis, author.
Luque, Alejandro, author.
Mondelo, Josep Maria, author.
Canadell, Marta, author.
Figueras, Jordi-Lluis, author.
Luque, Alejandro, author.
Mondelo, Josep Maria, author.
Series
Applied mathematical sciences (Springer-Verlag New York Inc.) ; v.195.
Available in Other Form
Print version: 9783319296609
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Table of Contents
An Overview of the Parameterization Method for Invariant Manifolds
Seminumerical Algorithms for Computing Invariant Manifolds of Vector Fields at Fixed Points
The Parameterization Method for Quasi-Periodic Systems: From Rigorous Results to Validated Numerics
The Parameterization Method in KAM Theory
A Newton-like Method for Computing Normally Hyperbolic Invariant Tori.
Seminumerical Algorithms for Computing Invariant Manifolds of Vector Fields at Fixed Points
The Parameterization Method for Quasi-Periodic Systems: From Rigorous Results to Validated Numerics
The Parameterization Method in KAM Theory
A Newton-like Method for Computing Normally Hyperbolic Invariant Tori.