PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Dmitri Burago, Anatole Katok, Mari Royer, Yakov Pesin.

Title:Geometry Working Seminar: Interpretation and applications of topological entropy in geometry
Seminar:Center for Dynamics and Geometry Seminars
Speaker:Dan Thompson, Penn State
Abstract:
Interpretation: The topological entropy is one of the key invariants in the theory of dynamical systems. When the dynamical system is a geodesic flow on a negatively curved manifold, it is good to know that the topological entropy has a very natural formulation as a geometric quantity. It is the exponential growth rate of volume in the universal cover. I'll sketch the classic proof of this fact which is due to Manning. Application: I'll sketch A. Katok's classic proof of his fascinating result which tells us that the topological entropy can be used to characterize which metrics on a surface are hyperbolic. More precisely, the topological entropy of the geodesic flow is minimised at the constant curvature metrics.

Room Reservation Information

Room Number:MB106
Date:02 / 10 / 2010
Time:03:30pm - 05:30pm