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 Seminar|
|Speaker:||Dan Thompson, Penn State|
|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
|Date:||02 / 10 / 2010|
|Time:||03:30pm - 05:30pm|