PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Anatole Katok.

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
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