Related papers: Transitive Anosov flows on non-compact manifolds

In this paper, we define $C^1$-robust transitivity for actions of $\RR^2$ on closed connected orientable manifolds. We prove that if the ambient manifold is three dimensional and the dense orbit of a robustly transitive action is not…

In this article we construct an expansive homeomorphism of a compact three-dimensional manifold with a fixed point whose local stable set is not locally connected. This homeomorphism is obtained as a topological perturbation of a…

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 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…

In this paper, we prove that finite-dimensional topological flows without fixed points and having a countable number of periodic orbits, have the small flow boundary property. This enables us to answer positively a question of Bowen and…

We prove that for any partially hyperbolic diffeomorphism with one dimensional neutral center on a 3-manifold, the center stable and center unstable foliations are complete; moreover, each leaf of center stable and center unstable…

This paper gives a complete classification of the possible ergodic decompositions for certain open families of volume-preserving partially hyperbolic diffeomorphisms. These families include systems with compact center leaves and…

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…

This paper is an exposition of the major results of P. Eberlein's paper, "When is a geodesic flow of Anosov type? I," in the special case when the manifold $M$ is a surface. We follow Eberlein's coverage closely, adding details when…

The aim of this paper is to study growth properties of group extensions of hyperbolic dynamical systems, where we do not assume that the extension satisfies the symmetry conditions seen, for example, in the work of Stadlbauer on symmetric…

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…

Building on the work of Eliashberg and Thurston, we associate to a taut foliation on a closed oriented $3$-manifold $M$ a Liouville structure on the thickening $[-1,1] \times M$, under suitable hypotheses. Our main result shows that this…

Let $v$ be a continuous flow with arbitrary singularities on a compact surface. Then we show that if $v$ is non-wandering then $v$ is topologically equivalent to a $C^{\infty}$ flow such that there are no exceptional orbits and $\mathrm{P}…

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…

The paper is devoted to the study of topological properties, structure and classification of Morse flows with fixed points on the boundary of three-dimensional manifolds. We construct a complete topological invariant of a Morse flow,…

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 provide a new criterion for the existence of a global cross section to a volume-preserving Anosov flow. The criterion is expressed in terms of expansion and contraction rates of the flow and is more general than the previous results of…

We prove Calegari's conjecture that every quasigeodesic flow on a closed hyperbolic 3-manifold can be deformed to a flow that is simultaneously quasigeodesic and pseudo-Anosov.

We study Hamiltonian diffeomorphisms of closed symplectic manifolds with non-contractible periodic orbits. In a variety of settings, we show that the presence of one non-contractible periodic orbit of a Hamiltonian diffeomorphism of a…

Despite the invertible setting, Anosov endomorphisms may have infinitely many unstable directions. Here we prove, under transitivity assumption, that an Anosov endomorphism on a closed manifold $M,$ is either special (that is, every $x \in…