Entropy, chaos and weak Horseshoe for infinite dimensional Random dynamical systems

Wednesday, October 24, 2012 - 10:15am - 11:05am
Keller 3-180
Wen Huang (University of Science and Technology of China)
In this talk, we present an answer to the long standing problem on the
implication of positive entropy of a random dynamical system. We study
C^0 infinite dimensional random dynamical systems in a Polish space, do not
assume any hyperbolicity, and prove that chaos and weak horseshoe exist
inside the random invariant set when its entropy is positive. This result
is new even for finite dimensional random dynamical systems and infinite
dimensional deterministic dynamical systems generated by either parabolic
PDEs or hyperbolic PDEs. We mention that in general one does not expect
to have a horseshoe without assuming hyperbolicity. For example, consider
the product system of a circle diffeomorphism with an irrational rotation
number and a system with positive entropy. This product system has positive
entropy and a weak horseshoe, but has no horseshoe.

This is a joint work with Prof. Kening Lu
MSC Code: