Bob Rink: What is the parametrization method in dynamical systems? скачать в хорошем качестве

Bob Rink: What is the parametrization method in dynamical systems?

Abstract: The parametrization method is a tool to compute invariant manifolds in dynamical systems, such as periodic orbits, (un-)stable manifolds, slow manifolds and invariant tori. The idea behind the method is simple: it works by (algorithmically) finding an embedding of the invariant manifold together with a representation of its dynamics in a coordinate chart. De La Llave et al realized that the method can nicely be combined with ideas from rigorous numerics, to provide computer-assisted proofs for the existence of invariant manifolds. Others, including myself, have used the method to compute high-precision approximations of the dynamics on the invariant manifolds. I will discuss both approaches, starting with the basics and finishing with an unpublished result on high-order phase reduction. Speaker bio: Bob Rink is a professor of mathematical analysis at the Vrije Universiteit Amsterdam, The Netherlands. He obtained his PhD in 2003 from Utrecht University, after which he was an EPSRC postdoctoral fellow at Imperial College London. He came to the Vrije Universiteit Amsterdam in 2007, where he became full professor in 2016. His research is in various directions of dynamical systems, with a focus on network dynamics and bifurcation theory.