Parameterization Method for Invariant Manifolds

From Rigorous Results to Effective Computations

AvÀlex Haro,Marta Canadell

Häftad, Engelska, 2018

Del 195 i serien Applied Mathematical Sciences

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2018-04-22
Mått:155 x 235 x 16 mm
Vikt:435 g
Format:Häftad
Språk:Engelska
Serie:Applied Mathematical Sciences
Antal sidor:267
Förlag:Springer International Publishing AG
ISBN:9783319806204

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Recensioner i media

“This book provides a unified formulation of the parametrization method (PM), which can be used to study different problems in the theory of dynamical systems. … The monograph can be recommended to mathematicians, scientists and engineers who are interested in the theory and application of dynamical systems as a reference book. It can also be used as a textbook for graduate students in courses on the mathematical theory of dynamical systems.” (Martin Hermann, Mathematical Reviews, March, 2017) “In this monograph, the authors present a unified formulation of the parametrization method applied in some specific contexts … . The monograph contains an extensive bibliography and is recommended to researchers specialized in the theoretical and computational methods for the study of dynamical systems.” (Rodica Luca, zbMATH, 1372.37002, 2017)

Innehållsförteckning

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.