BYU

Abstract by Xue Liu

Personal Infomation


Presenter's Name

Xue Liu

Degree Level

Doctorate

Abstract Infomation


Department

Mathematics

Faculty Advisor

Kening Lu

Title

Random exponential dichotomies, the random shadowing lemma and applications

Abstract

In this paper, we conisder general C^2 random dynamical system on Riemannian manifold. We define random hyperbolic set for a random dynamical system by using random exponential dichotomy. After introducing the point in the graph sense, we can prove a kind of random shadowing lemma which is different with the previous work. Under some specific condition, we also can prove there exists a strong full random horseshoe nearby a orbits of a  random homoclinic  points that is also a random version of the Birkhoff-smale theorem.