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Applied Mathematical Sciences

The Parameterization Method for Invariant Manifolds

From Rigorous Results to Effective Computations

Authors: Haro, À., Canadell, M., Figueras, J.-L., Luque, A., Mondelo, J.M.

  • 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
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eBook $84.99
price for USA (gross)
  • ISBN 978-3-319-29662-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-319-29660-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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.

Table of contents (5 chapters)

  • An Overview of the Parameterization Method for Invariant Manifolds

    Haro, Àlex

    Pages 1-28

  • Seminumerical Algorithms for Computing Invariant Manifolds of Vector Fields at Fixed Points

    Haro, Àlex (et al.)

    Pages 29-73

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

    Figueras, Jordi-Lluís (et al.)

    Pages 75-117

  • The Parameterization Method in KAM Theory

    Haro, Àlex (et al.)

    Pages 119-185

  • A Newton-like Method for Computing Normally Hyperbolic Invariant Tori

    Canadell, Marta (et al.)

    Pages 187-238

Buy this book

eBook $84.99
price for USA (gross)
  • ISBN 978-3-319-29662-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-319-29660-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Parameterization Method for Invariant Manifolds
Book Subtitle
From Rigorous Results to Effective Computations
Authors
Series Title
Applied Mathematical Sciences
Series Volume
195
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-29662-3
DOI
10.1007/978-3-319-29662-3
Hardcover ISBN
978-3-319-29660-9
Series ISSN
0066-5452
Edition Number
1
Number of Pages
XVI, 267
Number of Illustrations and Tables
3 b/w illustrations, 55 illustrations in colour
Topics