相关论文: On Invariant volumes of codimension-one Anosov flo…

We give a new proof of the existence of compact surfaces embedded in $R^3$ with Anosov geodesic flows. This proof starts with a non-compact model surface whose geodesic flow is shown to be Anosov using a uniformly strictly invariant cone…

In this paper, we describe a new approach to the problem of classification of transitive Anosov flows on 3-manifolds up to orbital equivalence. More specifically, generalizing the notion of Markov partition, we introduce the notion of…

This paper develops a family of Hofer-like metrics ($\dAnV{V}$) on the space of Anosov vector fields $\An(M)$, providing dynamically relevant distances based on the cost of deformation paths using $\Ck{k}$ or Sobolev $\SobolevHk{k}$ norms.…

In this article, we study the dynamics of geodesic flows on Riemannian (not necessarily compact) manifolds with no conjugate points. We prove the Anosov Closing Lemma, the local product structure, and the transitivity of the geodesic flows…

In this paper, we consider codimension one Anosov actions of IR^k, k ? 1, on closed connected orientable manifolds of dimension n+k with n? 3. We show that the fundamental group of the ambient manifold is solvable if and only if the weak…

A {\em sectional-Anosov flow} is a vector field on a compact manifold inwardly transverse to the boundary such that the maximal invariant set is sectional-hyperbolic (in the sense of \cite{mm}). We prove that any $C^2$ transitive…

A long-standing conjecture asserts that any Anosov diffeomorphism of a closed manifold is finitely covered by a diffeomorphism which is topologically conjugate to a hyperbolic automorphism of a nilpotent manifold. In this paper, we show…

A smooth Anosov flow on a closed oriented three manifold $M$ gives rise to a Liouville structure on the four manifold $[-1,1]\times M$ which is not Weinstein, by a construction of Mitsumatsu and Hozoori. We call it the associated Anosov…

This paper gives 3 different proofs (independently obtained by the 3 authors) of the following fact: given an Anosov flow on an oriented 3 manifold, the existence of a positive Birkhoff section is equivalent to the fact that the flow is…

We prove that every 3-manifold possesses a $C^1$, volume-preserving flow with no fixed points and no closed trajectories. The main construction is a volume-preserving version of the Schweitzer plug. We also prove that every 3-manifold…

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 present a combinatorial approach to the existence of foliations and contact structures transverse to a given pseudo-Anosov flow. Let $\varphi$ be a transitive pseudo-Anosov flow on a closed oriented 3-manifold. Our main technical result…

We introduce a new object, the dynamical torsion, which extends the potentially ill-defined value at $0$ of the Ruelle zeta function of a contact Anosov flow twisted by an acyclic representation of the fundamental group. We show important…

In this short note we prove that if a symplectomorphism f is C1-stably shadowable, then f is Anosov. The same result is obtained for volume-preserving diffeomorphisms.

Let f be a volume-preserving diffeomorphism of a closed C1 n-dimensional Riemannian manifold M: In this paper, we prove the equivalence between the following conditions: (a) f belongs to the C1-interior of the set of volume-preserving…

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…

Let $(M,g)$ be a $C^{\infty}$ compact, boudaryless connected manifold without conjugate points with quasi-convex universal covering and divergent geodesic rays. We show that the geodesic flow of $(M,g)$ is $C^{2}$-structurally stable from…

We discuss a metric description of the divergence of a (projectively) Anosov flow in dimension 3, in terms of its associated growth rates and give metric and contact geometric characterizations of when a projectively Anosov flow is Anosov.…

In this paper, we study transversely holomorphic partially hyperbolic flows, i.e. those whose holonomy pseudo-group is given by biholomorphic maps. We prove in the seven-dimensional case that under the assumption that the subcenter…

We prove that every sectional Anosov flow (or, equivalently, every sectional-hyperbolic attracting set of a flow) on a compact manifold has a periodic orbit. This extends the previous three-dimensional result obtained in [Existence of…