arXiv research

Extends Hopf-Tsuji-Sullivan dichotomy to higher rank groups and applies to Anosov subgroups.

Anosov groups' measures on limit sets are uniquely determined by their dimension.

The paper studies ergodicity of flows on subspaces, generalizing earlier work.

The paper develops a theory of conformal density at infinity for groups with contracting elements.

Let $X$ be a Hadamard manifold, and $Γ$ a non-elementary discrete group of isometries of $X$ which contains a rank one isometry. We relate the ergodic theory of the geodesic flow of the quotient orbifold $M=X/Γ$ to the behavior of the Poincar{é} series of $Γ$. Precisely, the aim of this paper is to extend the so-called…

Unique entropy measure found for convex projective manifolds.

The paper studies proper discontinuity of actions on Weyl chamber flow spaces.

Study ergodic properties of geodesic flows on specific manifolds without conjugate points.