The Parameterization Method for Invariant Manifolds

From Rigorous Results to Effective Computations

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Science, Physics, General Physics
Cover of the book The Parameterization Method for Invariant Manifolds by Àlex Haro, Marta Canadell, Jordi-Lluis Figueras, Alejandro Luque, Josep Maria Mondelo, Springer International Publishing
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Author: Àlex Haro, Marta Canadell, Jordi-Lluis Figueras, Alejandro Luque, Josep Maria Mondelo ISBN: 9783319296623
Publisher: Springer International Publishing Publication: April 18, 2016
Imprint: Springer Language: English
Author: Àlex Haro, Marta Canadell, Jordi-Lluis Figueras, Alejandro Luque, Josep Maria Mondelo
ISBN: 9783319296623
Publisher: Springer International Publishing
Publication: April 18, 2016
Imprint: Springer
Language: English

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.

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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.

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