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

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 are motivated by a conjecture of A. and S. Katok to study the smooth cohomologies of a family of Weyl chamber flows. The conjecture is a natural generalization of the Livshitz Theorem to Anosov actions by higher-rank abelian groups; it…

We introduce the matching functions technique in the setting of Anosov flows. Then we observe that simple periodic cycle functionals (also known as temporal distance functions) provide a source of matching functions for conjugate Anosov…

The goal of this paper is to explore the relationship between the geometric properties of an Anosov flow on a closed manifold $M$ and the analytic properties of its infinitesimal generator $X$ as a linear operator on the space of smooth…

The main result of this work is the following: for volume preserving flows on compact manifolds with the $C^r$ topology, $1 \leqq r \leqq \infty$ , the closure of every invariant manifold of periodic orbits and singularities is a chain…

We consider extensions of Anosov diffeomorphisms of an infranilmanifold by the real vector space R^{\omega}. Our main result, based on the analogous theorem in finite dimensions proven by Nitica and Pollicott, is that any Holder cocycle…

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…

Let $M$ be a closed $3$-dimensional Riemann manifold and let $3\le r\le \infty$. We prove that there exists an open dense subset in the space of $C^r$ volume-preserving Anosov flows on $M$ such that all the flows in it are exponentially…

Let f be a volume-preserving diffeomorphism of a closed C^\infty 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…

We prove that in dimension 3, Anosov flows which are $\mathbb{R}$-covered and skewed are orbit equivalent to Reeb-Anosov flows. We characterize the existence of an invariant contact form or of a Birkhoff section with a given boundary, in…

For any $C^\infty$, area-preserving Anosov diffeomorphism $f$ of a surface, we show that a suspension flow over $f$ is $C^\infty$-conjugate to a constant-time suspension flow of a hyperbolic automorphism of the two torus if and only if the…

Two flows are topologically almost commensurable if, up to removing finitely many periodic orbits and taking finite coverings, they are topologically equivalent. We prove that all suspensions of automorphisms of the 2-dimensional torus and…

For an endomorphism it is known that if all the points in the manifold have dense sets of pre-images then the dynamical system is transitive. The inverse has been shown for a residual set of points but the the exact inverse has not yet been…

We consider the class of partially hyperbolic diffeomorphisms on a closed 3-manifold with quasi-isometric center. Under the non-wandering condition, we prove that the diffeomorphisms are accessible if there is no $su$-torus. As a…

In this paper, we prove that manifolds of finite volume with Anosov geodesic flow have dense periodic orbits. The same result works for conservative Anosov flows in non-compact cases.

We study smooth volume-preserving perturbations of the time-1 map of the geodesic flow $\psi_{t}$ of a closed Riemannian manifold of dimension at least three with constant negative curvature. We show that such a perturbation has equal…

A pseudo-Anosov homeomorphism of a surface is a canonical representative of its mapping class. In this paper, we explain that a transitive pseudo-Anosov flow is similarly a canonical representative of its stable Hamiltonian class. It…

We construct Anosov flows in certain circle bundles over closed hyperbolic 3-manifolds, producing counterexamples to a conjecture of Verjovsky. Some of these 4-manifolds admit infinitely many distinct Anosov flows up to orbit equivalence.…

Let $X_1^t$ and $X_2^t$ be volume preserving Anosov flows on a 3-dimensional manifold $M$. We prove that if $X_1^t$ and $X_2^t$ are $C^0$ conjugate then the conjugacy is, in fact, smooth, unless $M$ is a mapping torus of an Anosov…

We prove by methods of harmonic analysis a result on existence of solutions for twisted cohomological equations on translation surfaces with loss of derivatives at most 3+ in Sobolev spaces. As a consequence we prove that product…