Unstable dimension variability and its relation with invariant probability distributions

Datum

16.12.2015

Zeit

11:00 - 12:00

Sprecher

Katrin Gelfert

Zugehörigkeit

Universidade Federal de Rio de Janeiro, Brasil

Sprache

en

Hauptthema

Physik

Andere Themen

Physik

Host

Holger Kantz

Beschreibung

When analyzing quantifiers for dynamical systems such as topological entropy, Lyapunov exponents, Birkhoff averages of test functions, in many cases computations are based on an analysis of periodic orbits. This, in a certain sense, is also what happens in a rigorous approach when trying to mathematically prove results about a qualitative and quantitative behavior of a dynamical system. For chaotic (uniformly hyperbolic) systems this goes through without problem. However, in more general cases, such an approach has certain possible pitfalls. In general systems, even when some hyperbolicity is present, there may coexist chaotic saddles with variable unstable dimension as well as attractors and/or repellers. This has an immediate effect on the possible probability distributions which are left invariant by the system and can cause curious effects such as phase transitions. I will discuss some, mathematically rigorous, results about this intimate relation.

Letztmalig verändert: 16.12.2015, 08:44:51