The Parameterization Method for Invariant Manifolds: From Rigorous Results to Effective Computations

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Àlex Haro Marta Canadell

The Parameterization Method for Invariant Manifolds

From Rigorous Results to Effective Computations

Àlex Haro, Marta Canadell, Jordi-Lluis Figueras , Alejandro Luque

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English

Springer International Publishing AG
22 April 2018

Number systems; Calculus & mathematical analysis; Differential calculus & equations; Mathematical physics

Series: Applied Mathematical Sciences

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.

By: Àlex Haro, Marta Canadell, Jordi-Lluis Figueras, Alejandro Luque, Josep Maria Mondelo
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: Softcover reprint of the original 1st ed. 2016
Volume: 195
Dimensions: Height: 235mm, Width: 155mm, Spine: 15mm
Weight: 4.336kg
ISBN: 9783319806204
ISBN 10: 3319806203
Series: Applied Mathematical Sciences
Pages: 267
Publication Date: 22 April 2018
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Reviews for The Parameterization Method for Invariant Manifolds: From Rigorous Results to Effective Computations

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)