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

Thismonograph presents some theoretical and computational aspects of theparameterization method for invariant manifolds, focusing on the followingcontexts: invariant manifolds associated with fixed points, invariant tori inquasi-periodically forced systems, invariant tori in Hamiltonian systems andnormally hyperbolic invariant manifolds. This book provides algorithms ofcomputation and some practical details of their implementation. The methodologyis illustrated with 12 detailed examples, many of them well known in theliterature of numerical computation in dynamical systems. A public version of the software used for some of the examples is available online.Thebook is aimed at mathematicians, scientists and engineers interested in thetheory and applications of computational dynamical systems.