BYU

Abstract by Xueming Hui

Personal Infomation


Presenter's Name

Xueming Hui

Degree Level

Doctorate

Abstract Infomation


Department

Mathematics

Faculty Advisor

Todd Fisher

Title

TOPOLOGICAL PRESSURE FOR CONSERVATIVE C1-DIFFEOMORPHISMS WITH NO DOMINATED SPLITTING

Abstract

We prove three formulas for computing topological pressure of C1-generic conservative diffeomorphism with no dominated splitting and show the continuity of topological pressure with respect to these diffeomorphisms. We prove for these generic diffeomorphisms that there is no equilibrium states with positive measure theoretic entropy. In particular, for hyperbolic potentials, there is no equilibrium states.

For C1 generic conservative diffeomorphism on compact surfaces with no dominated splitting and φm(x) := − 1/m log∥Dxfm∥,m ∈ N, we show that there exist equilibrium states with zero entropy and there exists a transition point t0 for the one parameter family {tφm}t≥0, such that there is no equilibrium states for t ∈ [0,t0) and there is an equilibrium state for t ∈ [t0,+∞).