PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Anatole Katok, Mari Royer.

Title:Livshits - type theorems and applications, I.
Seminar:Working Seminar: Dynamics and its Working Tools
Speaker:Boris Kalinin, University of South Alabama, visiting Penn State
Abstract:
A. Livshits pioneered the study of cohomology for hyperbolic dynamical systems in the early 1970’s. The simplest question in this area is that of existence and regularity of a solution g(x) to a cohomological equation f (x) = g(T x)− g(x), where T : M → M is a hyperbolic dynamical system, say a transitive Anosov diffeomorphism, and f is a given function on M , usually Holder continuous or smooth. Equations of this type appear naturally in many areas of dynamics. For example, if f (x) is the logarithm of the Jacobian of T then solving this equation is equivalent to finding an absolutely continuous invariant measure for T . We will recall the fundamental results obtained by Livshits: ex- istence of a continuous solution when the natural periodic ob- structions vanish and continuity of any measurable solution. We will then turn to similar questions in a more general and difficult setting when the functions f and g take values in a group G.

Room Reservation Information

Room Number:MB216
Date:09 / 08 / 2009
Time:03:30pm - 06:00pm