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

• Main Authors: Haro, Àlex (Author), Canadell, Marta (Author), Figueras, Jordi-Lluis (Author), Luque, Alejandro (Author), Mondelo, Josep Maria (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Series: Applied Mathematical Sciences, 195
• Subjects: Mathematics.; Dynamics.; Ergodic theory.; Partial differential equations.; Numerical analysis.; Statistical physics.; Dynamical systems.; Dynamical Systems and Ergodic Theory.; Statistical Physics, Dynamical Systems and Complexity.; Numerical Analysis.; Partial Differential Equations.
• Physical Description: XVI, 267 p. 58 illus., 55 illus. in color. online resource.
• ISBN: 9783319296623
• ISSN: 0066-5452 ;

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.