Related papers: Hyperbolic SRB measures and the leaf condition

We consider a discrete dynamical system on a pseudo-Riemannian manifold and we determine the concept of a hyperbolic set for it. We insert a condition in the definition of a hyperbolic set which implies to the unique decomposition of a part…

We present a topological proof of the existence of invariant manifolds for maps with normally hyperbolic-like properties. The proof is conducted in the phase space of the system. In our approach we do not require that the map is a…

Let M be a closed 3-manifold that supports a partially hyperbolic diffeomorphism f. If $\pi_1(M)$ is nilpotent, the induced action of f on $H_1(M, R)$ is partially hyperbolic. If $\pi_1(M)$ is almost nilpotent or if $\pi_1(M)$ has…

In this paper, we study some intrinsic characterization of conformally compact manifolds. We show that, if a complete Riemannian manifold admits an essential set and its curvature tends to -1 at infinity in certain rate, then it is…

We prove that the (necessarily existing) pseudo-physical or SRB-like measures of C1 expanding dynamical systems on a compact Riemannian manifold satisfy Pesin entropy formula. We include examples of C1 (non C1 plus Holder) expanding maps on…

A noncompact (oriented) surface satisfies the condition $(\star)$ if their isolated ends are ''accumulated by genus''. We show that every surface satisfying this condition is homeomorfic to the leaf of a minimal codimension one foliation on…

It is well-known that it is possible to construct a partially hyperbolic diffeomorphism on the 3-torus in a similar way than in Kan's example. It has two hyperbolic physical measures with intermingled basins supported on two embedded tori…

Let $(M, \partial M)$ be a compact 3-manifold with boundary, which admits a convex co-compact hyperbolic metric. We consider the hyperbolic metrics on $M$ such that the boundary is smooth and strictly convex. We show that the induced…

For any C1 expanding map f of the circle we study the equilibrium states for the potential -log |f'|. We formulate a C1 generalization of Pesin's Entropy Formula that holds for all the SRB measures if they exist, and for all the…

Conformally compact asymptotically hyperbolic metrics have been intensively studied. The goal of this note is to understand what intrinsic conditions on a complete Riemannian manifold (M,g) will ensure that g is asymptotically hyperbolic in…

In this paper, we provide an example of a partially hyperbolic diffeomorphism with any finite number of physical measures when some Lyapunov exponent is 0 on the center.

We describe the "hyperbolic" properties of a riemann surface lamination M canonically associated to every compact three manifolds of curvature less than 1. More precisely, if the geodesic flow is the phase space attached to an ordinary…

We obtain the following dichotomy for accessible partially hyperbolic diffeomorphisms of 3-dimensional manifolds having compact center leaves: either there is a unique entropy maximizing measure, this measure has the Bernoulli property and…

According to the work of Dennis Sullivan, there exists a smooth flow on the 5-sphere all of whose orbits are periodic although there is no uniform bound on their periods. The question addressed in this article is whether these type of…

We show that given two hyperbolic Dirichlet to Neumann maps associated to two Riemannian metrics of a Riemannian manifold with boundary which coincide near the boundary are close then the lens data of the two metrics is the same. As a…

We give geometric conditions that are necessary and sufficient for the existence of Sinai-Ruelle-Bowen (SRB) measures for $C^{1+\alpha}$ surface diffeomorphisms, thus proving a version of the Viana conjecture. As part of our argument we…

The bending map of a hyperbolic 3-manifold with boundary maps a geometrically hyperbolic metric to its bending measured geodesic lamination. We show that the bending map is proper. As a byproduct of the proof we show that the group of…

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.…

We prove that every unstable equivariant minimal surface in $\mathbb{R}^n$ produces a maximal representation of a surface group into $\prod_{i=1}^n\textrm{PSL}(2,\mathbb{R})$ together with an unstable minimal surface in the corresponding…

For any C1 diffeomorphism with dominated splitting we consider a nonempty set of invariant measures which describes the asymptotic statistics of Lebesgue-almost all orbits. They are the limits of convergent subsequences of averages of the…