Tianyuan Mathematical Center
in Southwest China

2018 Thematic Program (II)

Random dynamical systems and random attractors

[TMCSC]

June 17-20, 2018

W303  School of Mathematics, Sichuan University

SPEAKER

Hans Crauel (Goethe-Universitat)

ABSTRCT

For deterministic systems with nontrivial limit behaviour the concept of attractors has turned out to be useful. In order to incorporate random influences into the mathematical model one may use random dynamical systems (RDS). The notion of a random attractor for an RDS has been introduced in the early nineties of the last century, and it has found a lot of interest. RDS and random attractors are introduced and discussed, and some major results are described. For instance, random attractors of small random perturbations of a deterministic system may be considerably smaller than the attractor of the deterministic system. Furthermore, probabilistic characterizations of strong and weak random attractors are described. While set attractors – i.e. attractors for compact or bounded sets – are unique, this is in general not the case for point attractors. A recent result shows that there is always a unique minimal attractor provided an attractor exists at all.

ORGANIZERS

Kening Lu (Sichuan University)

Weinian Zhang (Sichuan University)

Wen Huang (Sichuan University)

Zeng Lian (Sichuan University)

Xiaohu Wang (Sichuan University)

Linfeng Zhou (Sichuan University)

Jun Shen (Sichuan University)

SUPPORTED BY

Tianyuan Mathematical Center in Southwest China

School of Mathematics, Sichuan University