Authors:
- Includes computational algorithms and practical details of implementation
- Illustrates implementation of the parameterization method with 12 fully detailed examples throughout the book
- Content covers theoretical and computational aspects of the paramerterization method
- Access to codes available via webpage
Part of the book series: Applied Mathematical Sciences (AMS, volume 195)
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Table of contents (5 chapters)
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Front Matter
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Back Matter
About this book
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.
Reviews
“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)
Authors and Affiliations
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Dept de Matem`atiques i Inform`atica, Barcelona Graduate School of Mathematics, Barcelona, Spain
Àlex Haro
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Brown University, ICERM, Providence, USA
Marta Canadell
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Uppsala University, Department of Mathematics, Uppsala, Sweden
Jordi-Lluis Figueras
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Consejo Superior de Investigaciones Cie, Instituto de Ciencias Matem´aticas, Madrid, Spain
Alejandro Luque
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Dept de Matem`atiques Universitat Aut`on, Institut d’Estudis Espacials de Cataluny, Bellaterra, Spain
Josep Maria Mondelo
Bibliographic Information
Book Title: The Parameterization Method for Invariant Manifolds
Book Subtitle: From Rigorous Results to Effective Computations
Authors: Àlex Haro, Marta Canadell, Jordi-Lluis Figueras, Alejandro Luque, Josep Maria Mondelo
Series Title: Applied Mathematical Sciences
DOI: https://doi.org/10.1007/978-3-319-29662-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-29660-9Published: 26 April 2016
Softcover ISBN: 978-3-319-80620-4Published: 22 April 2018
eBook ISBN: 978-3-319-29662-3Published: 18 April 2016
Series ISSN: 0066-5452
Series E-ISSN: 2196-968X
Edition Number: 1
Number of Pages: XVI, 267
Number of Illustrations: 3 b/w illustrations, 55 illustrations in colour
Topics: Dynamical Systems and Ergodic Theory, Complex Systems, Numerical Analysis, Partial Differential Equations, Statistical Physics and Dynamical Systems