PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

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

Title:Multifractal analysis of Birkhoff averages for non-uniformly expanding maps and countable Markov maps
Seminar:Center for Dynamics and Geometry Seminars
Speaker:Thomas Jordan, University of Bristol, UK
Abstract:
The multifractal analysis for Birkhoff averages for expanding maps of the interval is now well understood. This involves fixing a continuous potential at looking at the dimension of the level sets where the Birkhoff average of the potential is $\alpha$. We will look at the two generalisations of this situation. One case is where parabolic fixed points (sometimes called indifferent fixed points) are allowed. This allows maps such as the Farey map and the Manneville-Pomeau maps to be studied. The second generalisation is to countable state Markov maps such as the Gauss map. We will illustrate the differences between these cases and the uniformly hyperbolic case. This talk contains two pieces of joint work one with Anders Johansson, Anders Oberg and Mark Pollicott and the other with Godofredo Iommi.

Room Reservation Information

Room Number:MB106
Date:04 / 05 / 2010
Time:03:30pm - 05:30pm