Parameterization Method for Invariant Manifolds

• 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.

“This book provides a unified formulation of the parametrization method (PM), which can be used to study different problems in the theory of dynamical systems. … The monograph can be recommended to mathematicians, scientists and engineers who are interested in the theory and application of dynamical systems as a reference book. It can also be used as a textbook for graduate students in courses on the mathematical theory of dynamical systems.” (Martin Hermann, Mathematical Reviews, March, 2017)  “In this monograph, the authors present a unified formulation of the parametrization method applied in some specific contexts … . The monograph contains an extensive bibliography and is recommended to researchers specialized in the theoretical and computational methods for the study of dynamical systems.” (Rodica Luca, zbMATH, 1372.37002, 2017)