相关论文: Regular projectively Anosov flows on three-dimensi…

We give complete classification of C^2-regular and non-degenerate projectively Anosov flows on three dimensional manifolds. More precisely, we prove that such a flow on a connected manifold must be either an Anosov flow or represented as a…

In this article we study topological transitivity of Anosov flows on non-compact 3-manifolds. We provide homological conditions under which the lifts of a transitive Anosov flow to certain infinite covers of the manifold remain transitive.…

We study (topological) pseudo-Anosov flows from the perspective of the associated group actions on their orbit spaces and boundary at infinity. We extend the definition of Anosov-like action from [BFM22] from the transitive to the general…

For Anosov flows obtained by suspensions of Anosov diffeomorphisms on surfaces, we show the following type of rigidity result: if a topological conjugacy between them is differentiable at a point, then the conjugacy has a smooth extension…

In this paper, we study transversely holomorphic flows, i.e. those whose holonomy pseudo-group is given by biholomorphic maps. We prove that for Anosov flows on smooth compact manifolds, the strong unstable (respectively, stable)…

We show that the action on its orbit space induced by a pseudo-Anosov flow on a closed $3$-manifold (and more general Anosov-like actions) can be seen as an isometric action on a Gromov-hyperbolic space. When the flow is not $\R$-covered,…

In this article we analyze totally periodic pseudo-Anosov flows in graph three manifolds. This means that in each Seifert fibered piece of the torus decomposition, the free homotopy class of regular fibers has a finite power which is also a…

We prove that every transitive topologically Anosov flow on a closed 3-manifold is orbitally equivalent to a smooth Anosov flow, preserving an ergodic smooth volume form.

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…

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…

We consider two transitive $3$-dimensional Anosov flows which do not preserve volume and which are continuously conjugate to each other. Then, disregarding certain exceptional cases, such as flows with $C^1$ regular stable or unstable…

In this text we (re)-tell the theory of pseudo-Anosov flows on 3-manifolds with the orbit space as the central character; via a streamlined framework called {\em Anosov-like group actions}. This brings a simplified and unified perspective,…

We prove that every sectional-Anosov flow of a compact 3-manifold $M$ exhibits a finite collection of hyperbolic attractors and singularities whose basins form a dense subset of $M$. Applications to the dynamics of sectional-Anosov flows on…

We prove that a $C^2$-generic Riemannian metric on a closed surface has either an elliptic closed geodesic or an Anosov geodesic flow. As a consequence, we prove the $C^2$-stability conjecture for Riemannian geodesic flows of closed…

We construct non-algebraic Anosov flows in dimension $3+2n$, $n\geq 2$, by suspending the action of the fundamental group of a finite cover of the Bonatti-Langevin flow.

Building upon the work of Mitsumatsu and Hozoori, we establish a complete homotopy correspondence between three-dimensional Anosov flows and certain pairs of contact forms that we call Anosov Liouville pairs. We show a similar…

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 apply the matching functions technique in the setting of contact Anosov flows which satisfy a bunching assumption. This allows us to generalize the 3-dimensional rigidity result of Feldman-Ornstein~\cite{FO}. Namely, we show that if two…

The main result is that if an Anosov flow in a closed hyperbolic three manifold is not R-covered, then the flow is a quasigeodesic flow. We also prove that if a hyperbolic three manifold supports an Anosov flow, then up to a double cover it…

Given an Anosov flow on a closed 3-manifold, we are interested in the problem of whether or not making non-trivial Fried surgeries along a finite set of periodic orbits can produce a flow equivalent to itself. We show that for some…