Abstract by Xueming Hui

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Presenter's Name

Xueming Hui

Degree Level


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Faculty Advisor

Todd Fisher


Toplogical pressure for conservative C^1-diffeomorphisms with no dominated splitting


We prove three formulas for computing topological pressure of C1-generic conservative diffeomorphism 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 family {tφm(x)}t≥0, such that there is an equilibrium states for t ∈ [0,t0) and there is an equilibrium state for t ∈ [t0,+∞).