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.

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...

Table of Contents:

• An Overview of the Parameterization Method for Invariant Manifolds
• Seminumerical Algorithms for Computing Invariant Manifolds of Vector Fields at Fixed Points
• The Parameterization Method for Quasi-Periodic Systems: From Rigorous Results to Validated Numerics
• The Parameterization Method in KAM Theory
• A Newton-like Method for Computing Normally Hyperbolic Invariant Tori.