Related papers: Dominated splitting and zero volume for incompress…

We classify quasiconformal Anosov flows whose strong stable and unstable distributions are at least two dimensional and the sum of these two distributions is smooth. We deduce from this classification result the complete classification of…

We show that every volume preserving codimension one Anosov flow on a closed Riemannian manifold of dimension greater than three admits a global cross section and is therefore topologically conjugate to a suspension of a linear toral…

The main result of this article is that if a $3$-manifold $M$ supports an Anosov flow, then the number of conjugacy classes in the fundamental group of $M$ grows exponentially fast with the length of the shortest orbit representative,…

For a transitive Anosov flow $\Phi$ on 3-dimensional closed manifold $M$ , we realize its Teichm\"uller space in the sense of smooth orbit-equivalence classes as a product of two function spaces. As an application, we show the…

Let $(M, g)$ be a complete Riemannian manifold without focal points and curvature bounded below. We prove that when the average of the sectional curvature in tangent planes along geodesics is negative and uniformly away from zero, then the…

Let F be a foliation in a closed 3-manifold with negatively curved fundamental group and suppose that F is almost transverse to a quasigeodesic pseudo-Anosov flow. We show that the leaves of the foliation in the universal cover extend…

We prove a result allowing to build (transitive or non-transitive) Anosov flows on 3-manifolds by gluing together filtrating neighborhoods of hyperbolic sets. We give several applications; for example: 1. we build a 3-manifold supporting…

The first half of this paper is concerned with the topology of the space $\AAA(M)$ of (not necessarily contact) Anosov vector fields on the unit tangent bundle $M$ of closed oriented hyperbolic surfaces $\Sigma$. We show that there are…

In this work, we provide two novel approaches to show that incompressible fluid flow in a finite domain contains at most a finite number vortices. We use a recently developed geometric theory of incompressible viscous flows along with an…

We study the transverse geometric behavior of 2-dimensional foliations in 3-manifolds. We show that an R-covered transversely orientable foliation with Gromov hyperbolic leaves in a closed 3-manifold admits a regulating, transverse…

We produce infinitely many examples of Anosov flows in closed 3-manifolds where the set of periodic orbits is partitioned into two infinite subsets. In one subset every closed orbit is freely homotopic to infinitely other closed orbits of…

We first prove rigidity results for pseudo-Anosov flows in prototypes of toroidal 3-manifolds: we show that a pseudo-Anosov flow in a Seifert fibered manifold is up to finite covers topologically equivalent to a geodesic flow and we show…

We study obstructions preventing a three-dimensional Anosov flow from serving as the base of a fiberwise Anosov flow. We prove a non-existence result if the base flow admits infinitely many periodic orbits in the same free homotopy class.…

A new infinitesimal characterization of completely positive but not necessarily homomorphic Markov flows from a C^*-algebra to bounded operators on the boson Fock space over L^2(R) is given. Contrarily to previous characterizations, based…

We study generic volume-preserving diffeomorphisms on compact manifolds. We show that the following property holds generically in the $C^1$ topology: Either there is at least one zero Lyapunov exponent at almost every point, or the set of…

This paper is devoted to higher dimensional Anosov flows and consists of two parts. In the first part, we investigate fiberwise Anosov flows on affine torus bundles which fiber over 3-dimensional Anosov flows. We provide a dichotomy result…

We show that the time-1 map of an Anosov flow, whose strong-unstable foliation is $C^2$ smooth and minimal, is $C^2$ close to a diffeomorphism having positive central Lyapunov exponent Lebesgue almost everywhere and a unique physical…

The purpose of this paper is to establish limit laws for volume preserving almost Anosov flows on $3$-three manifolds having a neutral periodic of cubic saddle type. In the process, we derive estimates for the Dulac maps for cubic neutral…

We prove that in a compact manifold of dimension $n\geq 2$, a $C^{1+\alpha}$ volume-preserving diffeomorphisms that are robustly transitive in the $C^1$-topology have a dominated splitting. Also we prove that for 3-dimensional compact…

We show that if X is a Venice mask (i.e. nontransitive sectional-Anosov flow with dense periodic orbits) supported on a compact 3-manifold, then the omega-limit set of every non-recurrent point in the unstable manifold of some singularity…