Using an approach due to Bowen, Franco showed that continuous expansive flows with
specification have unique equilibrium states for potentials with the Bowen property. We …

We prove that for closed surfaces M with Riemannian metrics without conjugate points and
genus≥ 2 the geodesic flow on the unit tangent bundle T 1 M has a unique measure of …

We show that C^∞-surface diffeomorphisms with positive topological entropy have finitely
many ergodic measures of maximal entropy in general, and exactly one in the topologically …

The Sinai billiard map $ T $ on the two-torus, ie, the periodic Lorentz gas, is a discontinuous
map. Assuming finite horizon, we propose a definition $ h_* $ for the topological entropy of …

In this article, we consider the geodesic flow on a compact rank $1 $ Riemannian manifold $
M $ without focal points, whose universal cover is denoted by $ X $. On the ideal boundary …

In this paper, we study dynamics of geodesic flows over closed surfaces of genus greater
than or equal to 2 without focal points. Especially, we prove that there is a large class of …

We construct symbolic dynamics for three dimensional flows with positive speed. More
precisely, for each $\chi> 0$, we code a set of full measure for every invariant probability …

Equilibrium states for geodesic flows over closed rank 1 manifolds were studied recently in
Burns, Climenhaga, Fisher, and Thompson [Geom. Funct. Anal. 28 (2018), no. 5, 1209 …

We introduce a gluing orbit property, weaker than specification, for both continuous maps
and flows. We prove that flows with the C 1-robust gluing orbit property are uniformly …

We show that $ C^\infty $ surface diffeomorphisms with positive topological entropy have at
most finitely many ergodic measures of maximal entropy in general, and at most one in the …