PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Stephen Simpson.

Title:Topological pressure for non-compact sets, Kamae entropy and Kolmogorov complexity
Seminar:Logic Seminar
Speaker:Daniel Thompson, Pennsylvania State University
Abstract:
For compact spaces, the theory of topological pressure and equilibrium states is a cornerstone of modern ergodic theory. It has long been thought desirable to generalize this theory to non-compact spaces. I will give a brief over-view of the various approaches to this problem in the literature and give an elementary alternative definition of topological pressure in the non-compact setting. It turns out that this definition is a generalization of the Kamae entropy. The definition assigns a non-negative number to each point in the space and can be interpreted as a sort of complexity. In Cantor space, this quantity is related to the Kolmogorov complexity. I will attempt to give an accessible explanation of the dynamical systems context of this theory. I will then describe some results by Brudno, Kamae, Van Lambalgen and White to illustrate the connection with Kolmogorov complexity and to demonstrate why this may be of interest to Logicians.

Room Reservation Information

Room Number:MB315
Date:11 / 30 / 2010
Time:02:30pm - 03:45pm