Related papers: Sectional-Anosov flows in higher dimensions

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…

We present a multidimensional flow exhibiting a Rovella-like attractor: a transitive invariant set with a non-Lorenz-like singularity accumulated by regular orbits and a multidimensional non-uniformly expanding invariant direction.…

In the present paper we study the C1-robustness of the three properties: average shadowing, asymptotic average shadowing and limit shadowing within two classes of conservative flows: the incompressible and the Hamiltonian ones. We obtain…

We introduce a new version of expansiveness for flows. Let $M$ be a compact Riemannian manifold without boundary and $X$ be a $C^1$ vector field on $M$ that generates a flow $\varphi_t$ on $M$. We call $X$ {\it rescaling expansive} on a…

We prove the transitivity of real Anosov diffeomorphisms, which are Anosov diffeomorphisms where stable and unstable spaces decompose into a continuous sum of invariant one-dimensional sub-spaces with uniform contraction/expansion over the…

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…

We prove that for any closed manifold of dimension 3 or greater that there is an open set of smooth flows that have a hyperbolic set that is not contained in a locally maximal one. Additionally, we show that the stabilization of the…

We build an example of a non-transitive, dynamically coherent partially hyperbolic diffeomorphism $f$ on a closed $3$-manifold with exponential growth in its fundamental group such that $f^n$ is not isotopic to the identity for all $n\neq…

It is known that sectional-hyperbolic attracting sets, for a $C^2$ flow on a finite dimensional compact manifold, have at most finitely many ergodic physical invariant probability measures. We prove an upper bound for the number of distinct…

In this article, we give a quasi-final classification of quasiconformal Anosov flows. We deduce a very interesting differentable rigidity result for the orbit foliations of hyperbolic manifold of dimension at least three.

In this paper, we prove that if the geodesic flow of a complete manifold without conjugate points with sectional curvatures bounded below by $-c^2$ is of Anosov type, then the constant of contraction of the flow is $\geq e^{-c}$. Moreover,…

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 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,…

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 every transitive dynamically coherent partially hyperbolic diffeomorphism with a one-dimensional center foliation $\W^c$ satisfying that $f(W)=W$ for every leaf $W\in \W^c$ is a discretized Anosov flow.

It is proved that the motion of a charge particle on a hyperbolic oriented two-dimensional surface in a magnetic field given by the volume form of the hyperbolic metric is completely integrable on the energy levels E < 1/2 in terms of…

In this paper, we define codimension one Anosov actions of $\RR^k, k\geq 2,$ on a closed connected orientable manifold $M$. We prove that if the ambient manifold has dimension greater than $k+2$, then the action is topologically transitive.…

It is given notions of singular hyperbolicity and sectional Lyapunov exponents of orders beyond the classical ones, namely, other dimensions besides the dimension 2 and the full dimension of the central subbundle of the singular hyperbolic…

For a partially hyperbolic splitting a $C^1$ vector field $X$ on a $m$-manifold $M$, we obtain singular hyperbolicity whether $E$ is one-dimensional subspace, based on the idea of cross products. We show the existence of adapted metrics for…

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…