Constructive Banach Space Methods for Studying Invariant Dynamics and Computer Assisted Analysis
I will present an overview of several methods for studying invariant sets of dynamical systems which are based on high order BanachSpace approximations and rigorously validated computer assisted error bounds. The key idea is to reformulate dynamical questions into questions about fixed points of certain operator equations. Then functional analytic methods are used to obtain approximate solutions of the operator equations. The defect associated with a given approximation is studied using rigorous computer assisted estimates. If the approximate solution is "good enough'' then it is often possible to conclude the existence of a true solution "nearby''. I will discuss some applications of these ideas to problems such as computing periodic orbits, invariant manifolds, and connecting orbits for differential equations.
Mercredi, 19 juin, 11h00
Salle Des Plaines A