Mathematics Colloquium-Prof. Yakov B. Pesin (The Pennsylvania State University), Equilibrium measures in hyperbolic dynamics via geometric measure theory
| When |
Oct 29, 2020
from 12:30 PM to 01:30 PM |
|---|---|
| Where | Via Zoom |
| Contact Name | Professor Shirshendu Chatterjee |
| Contact Phone | 1(212)650-5101 |
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- Prof. Yakov B. Pesin (The Pennsylvania State University), Equilibrium measures in hyperbolic dynamics via geometric measure theory
In the classical settings of Anosov diffeomorphisms or more general locally maximal hyperbolic sets I describe a new approach for constructing equilibrium measures which is pure geometrical in its nature and uses no symbolic representations of the system. As a result it can be used to effect thermodynamics formalism for systems for which no symbolic representation is available such as partially hyperbolic systems. This approach applies to a broad class of potentials satisfying Bowen’s property, which includes the usual class of Holder continuous potentials and it gives a new way for constructing measures of maximal entropy (first constructed in this setting by Margulis). It also reveals a crucial geometric property of equilibrium measures that has not been known before — the conditional measures they generate on unstable leaves are measures of full Caratheodory dimension — the fact that lies in the heart of the geometric approach. The talk is based on two joint work with V. Climenhaga and A. Zelerovich.
Zoom link: https://ccny.zoom.us/j/92057419965
For more information on this and future math colloquium events, please visit our website using the link below.
https://math.sci.ccny.cuny.edu/seminar/show/7
