Related papers: Periodic measures and partially hyperbolic homocli…

In this work we study the class of mostly expanding partially hyperbolic diffeomorphisms. We prove that such class is $C^r$-open, $r>1$, among the partially hyperbolic diffeomorphisms (in the narrow sense) and we prove that the mostly…

For Anosov diffeomorphisms on the $3$-torus which are strongly partially hyperbolic with expanding center, we construct systems of strong unstable and center stable Margulis measures which are holonomy-invariant. This allows us to obtain a…

We address the problem of existence and uniqueness (finite- ness) of ergodic equilibrium states for a natural class of partially hyperbolic dynamics homotopic to Anosov. We propose to study the disintegration of equilibrium states along…

We consider transitive Anosov diffeomorphisms for which every periodic orbit has only one positive and one negative Lyapunov exponent. We establish various properties of such systems including strong pinching, C^{1+\beta} smoothness of the…

We give a complete topological classification of transitive partially hyperbolic diffeomorphisms in 3-manifolds in terms of Anosov flows, completing a program proposed by Pujals. In particular, this also allows to give a full answer to the…

This paper introduces the concept of average conformal hyperbolic sets, which admit only one positive and one negative Lyapunov exponents for any ergodic measure. For an average conformal hyperbolic set of a C1 diffeomorphism, utilizing the…

We consider Hamiltonian diffeomorphisms of the Euclidean space, generated by compactly supported time-dependent perturbations of hyperbolic quadratic forms. We prove that, under some natural assumptions, such a diffeomorphism must have…

We study cohomology of Holder continuous linear cocycles over a hyperbolic dynamical system and regularity of conjugacy between Anosov systems. For cocycles $A$ and $B$ with conjugate periodic data, we establish Holder cohomology under…

Let $\Gamma$ be a non-elementary Gromov-hyperbolic group, and $\partial \Gamma$ denote its Gromov boundary. We consider $\Gamma$-invariant proper $\delta$-hyperbolic, quasi-convex metric $d$ on $\Gamma$, and the associated…

We consider the geodesic flow on a complete connected negatively curved manifold. We show that the set of invariant borel probability measures contains a dense $G_\delta$-subset consisting of ergodic measures fully supported on the…

This paper contains two parts. In the first part, we study the ergodicity of periodic measures of random dynamical systems on a separable Banach space. We obtain that the periodic measure of the continuous time skew-product dynamical system…

We show that for any $C^1$ partially hyperbolic diffeomorphism, there is a full volume subset, such that any Cesaro limit of any point in this subset satisfies the Pesin formula for partial entropy. This result has several important…

We study the existence of Anosov diffeomorphisms on complete open surfaces. We show that under the assumptions of density of periodic points and uniform geometry that such diffeomorphisms have a system of Margulis measures, which are a…

We construct examples of robustly transitive and stably ergodic partially hyperbolic diffeomorphisms $f$ on compact $3$-manifolds with fundamental groups of exponential growth such that $f^n$ is not homotopic to identity for all $n>0$.…

This paper presents a new construction of non-Anosov Partially Hyperbolic Geodesic flows. Our construction is closely related to the construction made by Carneiro and Pujals, the novelty is the use of conformal deformations to produce the…

We show that every transitive dynamically coherent partially hyperbolic diffeomorphism with a one-dimensional center foliation $\W^c$ satisfying that $f(W)=W$ for every leaf $W\in \W^c$ is a discretized Anosov flow.

We prove that there is a residual subset $\mathcal{S}$ in $\text{Diff}^1(M)$ such that, for every $f\in \mathcal{S}$, any homoclinic class of $f$ with invariant one dimensional central bundle containing saddles of different indices (i.e.…

Let $f$ be a $C^r$ surface diffeomorphism with large entropy (more precisely, $h_{\rm top}(f)>\lambda_{\min}(f)/{r}$). Then the number of ergodic measures of maximal entropy is upper semicontinuous at $f$. This generalizes the $C^\infty$…

Let $f:M\to M$ be a $C^{1+\epsilon}$-map on a smooth Riemannian manifold $M$ and let $\Lambda\subset M$ be a compact $f$-invariant locally maximal set. In this paper we obtain several results concerning the distribution of the periodic…

In this paper we revisit uniformly hyperbolic basic sets and the domination of Oseledets splittings at periodic points. We prove that periodic points with simple Lyapunov spectrum are dense in non-trivial basic pieces of Cr-residual…