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The Parameterization Method for Invariant Manifolds

From Rigorous Results to Effective Computations

  • Àlex Haro
  • Marta Canadell
  • Jordi-Lluis Figueras
  • Alejandro Luque
  • Josep Maria Mondelo

Part of the Applied Mathematical Sciences book series (AMS, volume 195)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Àlex Haro, Alejandro Luque
    Pages 119-185
  3. Back Matter
    Pages 239-267

About this book

Introduction

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.

Keywords

Parameterization Method Invariant Manifolds Quasi-periodically Forced Dynamical Systems KAM Theory Numerical Methods Automatic Differentiation Normally Hyperbolic Invariant Manifolds

Authors and affiliations

  • Àlex Haro
    • 1
  • Marta Canadell
    • 2
  • Jordi-Lluis Figueras
    • 3
  • Alejandro Luque
    • 4
  • Josep Maria Mondelo
    • 5
  1. 1.Dept de Matem`atiques i Inform`aticaBarcelona Graduate School of MathematicsBarcelonaSpain
  2. 2.Brown UniversityICERMProvidenceUSA
  3. 3.Uppsala UniversityDepartment of MathematicsUppsalaSweden
  4. 4.Consejo Superior de Investigaciones CieInstituto de Ciencias Matem´aticasMadridSpain
  5. 5.Dept de Matem`atiques Universitat Aut`onInstitut d’Estudis Espacials de CatalunyBellaterraSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-29662-3
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-29660-9
  • Online ISBN 978-3-319-29662-3
  • Series Print ISSN 0066-5452
  • Series Online ISSN 2196-968X
  • Buy this book on publisher's site
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