4 problems

Let $X$ be a conservative $C^1$ vector field and let $\Gamma$ be a singular hyperbolic set for $X$. A singular adapted metric is a Riemannian metric satisfying the contraction, dom…

Let $M$ be a compact manifold and let $r\in\mathbb N\cup\{\infty\}$. An iterated function system consists of a finite family of homeomorphisms of $M$; it is transitive if the semig…

Let $M$ be a compact Riemannian manifold, let $r$ be sufficiently large, and let $m\geq 2$ be an integer. An $m$-tuple of $C^r$ volume-preserving diffeomorphisms of $M$ is called…

Let $\Gamma$ be a group that is generic in an appropriate model for random groups, let $M$ be a compact manifold, and consider an action of $\Gamma$ on $M$. A smooth volume form is…