Research-Unstable entropies and Pressure of partially hyperbolic diffeomorphisms

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Unstable entropies and Pressure of partially hyperbolic diffeomorphisms

Speaker: Weisheng Wu (China Agricultural University)
Time: May 31, 2018, 11:00-12:00
Location: Conference Room 415, Wisdom Valley 3#

Abstract: Given a partially hyperbolic diffeomorphism, we introduce the notions of unstable metric entropy and unstable topological entropy. These notions coincide with the entropy defined by Ledrappier-Young and unstable volume growth rate considered by Hua-Saghin-Xia respectively. A variational principle can be established which states that unstable topological entropy is the supremum of unstable metric entropy taken over all invariant measures. Other properties such as upper semicontinuity of unstable entropy function will be also discussed. These results can be extended to the unstable pressure and the so-called u-equilibrium states can be investigated.