HOROWITZ SEMINAR

PROBABILITY, ERGODIC THEORY and DYNAMICAL SYSTEMS

Van Cyr (Penn State University)

will speak

Obstructions to the Existence of Equilibrium Measures for Countable Markov Shifts.

Abstract:

The goal of this talk is to present several new results aimed at showing:
1. In the space of all potentials on a countable Markov shift, the set of potentials that have a (generalized) equilibrium measure is supnorm-open and Lipschitz-dense.
2. There is a (simple) combinatorial condition on the shift which is necessary and sufficient for the complement of this set to be nonempty; "most" shifts satisfy it. In this case we show that, in a suitable topology, the phenomenon of transience is open and dense in this complement.

To suggest a talk (yours, or someone elses), contact Jon. Aaronson: aaro at post dot tau dot ac dot il

Back to: Jon Aaronson's homepage.

Last update on 20/1/09.