Seminari d’Anàlisi UAB-UB

Approximation in the Zygmund Class

17 / 02 / 2020

Speaker: Odí Soler, Universitat Autònoma de Barcelona
Time: 15:00
Place: Aula Petita (UAB-CRM)

Abstract

More Information: Seminari d’Anàlisi UAB-UB

Seminari de Sistemes Dinàmics UB-UPC

Some shadowing and inverse shadowing results

19 / 02 / 2020

Speaker: Dmitrii Todorov, Centre de Recerca Matemàtica
Time: 16:00
Place: Aula S01, Facultat de Matemàtiques i Estadística, UPC

Summary:

Among various types of stability properties for dynamical systems, there is class of "per-iteration" stability properties called "shadowing properties". A typical property like that would say that behavior of individual trajectories does not depend much on a constantly applied small perturbation. While it is not a surprise that such properties usually hold for simple systems with simple attractors (at least to some extent), they also do hold for some chaotic systems as well. It is well-known (and makes a part of stability conjecture proof) that uniformly hyperbolic systems have various nice shadowing properties. It would be desirable to be able to say the same for less strongly chaotic systems (e.g. because they are the ones that usually come from applications).
I will present some results somewhat destroying this hope.
This was a subject of my PhD and I have not worked on it for years by now. If time permits, I will say a couple of words about my more recent projects as well.