Robert Szczelina
(Jagelló Egyetem, Krakkó, Lengyelország)
A geometric method for computer assisted proofs in Delay Differential Equations
Absztrakt: I will do a short (geometric) introduction to the notion of covering relations and the topological methods based on them to prove existence
of interesting dynamics for maps between finite dimensional spaces. Then I will state similar results for compact maps over suitable but possibly
infinite spaces. I will use them to show how rigorous numerical methods can be applied to prove existence of apparently unstable periodic orbits
in the Mackey-Glass equation for classical values of parameters, where chaos was numerically observed. I will also show how to prove the
persistence of symbolic dynamics in some chaotic ODE perturbed to the delay differential equation (DDE).
