It is well known that on every $d$-dimensional torus there exists linear Anosov automorphisms. My question is the following: Given $k< d$ does there exists a linear Anosov au …

Let $M$ be a closed manifold, $m$ be the normalized volume measure on $M$, and $f:M\to M$ be a $C^2$ transitive Anosov diffeomorphism. Consider the pushforward $f^km$ defined by - …

Let $T: X \to X$ be an Anosov diffeomorphism. Suppose $f: X \to \mathbb{R}$ is Holder continuous (say with exponent $\alpha$). The question arises as to when $f$ can be written a …

Let $M$ be a compact Riemannian manifold and let $T : M \rightarrow M$ be Anosov. I have read here that it is an open problem to prove that $T$ is topologically mixing if $M$ is co …

Let $T_t$ be the geodesic flow on a surface $S$ of constant negative curvature, and let $M(f,t) := \langle \bar f \cdot (f \circ T_t) \rangle$, where $\langle f \rangle := \int_S f …

I'm trying to read a paper of Boris Kalinin on the cohomology of dynamical systems for a project. The material is geared towards topologically transitive Anosov diffeomorphisms (w …

My collaborators and I are studying certain rigidity properties of hyperbolic toral automorphisms. These are given by integral matrices A with determinant 1 and without eigenvalue …

Are there examples of codimension 2 foliations on simply connected compact 4-manifolds such that Every leaf is diffeomorphic to $\mathbb R^2$ Every leaf is dense? Same questio …