### Unique measure of maximal entropy for the finite horizon periodic Lorentz gas

- Series
- CDSNS Colloquium
- Time
- Monday, February 3, 2020 - 11:15 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Mark F. Demers – Fairfield University – mdemers@fairfield.edu

While the existence and properties of the SRB measure for the billiard map associated with a periodic Lorentz gas are well understood, there are few results regarding other types of measures for dispersing billiards. We begin by proposing a naive definition of topological entropy for the billiard map, and show that it is equivalent to several classical definitions. We then prove a variational principle for the topological entropy and proceed to construct a unique probability measure which achieves the maximum. This measure is Bernoulli and positive on open sets. An essential ingredient is a proof of the absolute continuity of the unstable foliation with respect to the measure of maximal entropy. This is joint work with Viviane Baladi.