Related papers: Transitive Anosov flows on non-compact manifolds

By constructing a non-empty domain of discontinuity in a suitable homogeneous space, we prove that every torsion-free projective Anosov subgroup is the monodromy group of a locally homogeneous contact Axiom A dynamical system with a unique…

For a compact three-dimensional smooth Riemannian manifold of strictly 1/4-pinched negative sectional curvature, we establish exponential mixing of the frame flow with respect to the normalized volume. More generally this result extends to…

We show that a transitive Anosov flow with orientable stable and unstable foliations that either (i) admits a Birkhoff section whose first return map is a Penner type pseudo-Anosov map, or (ii) is totally periodic admits a genus one…

In a neighborhood of a hyperbolic periodic orbit of a volume-preserving flow on a manifold of dimension 3, we define and show the existence of a normal form for the generator of the flow that encodes the dynamics. If the flow is a contact…

We prove a structure theorem for pseudo-Anosov flows restricted to Seifert fibered pieces of three manifolds. The piece is called periodic if there is a Seifert fibration so that a regular fiber is freely homotopic, up to powers, to a…

We study global aspects of the mean curvature flow of non-separating hypersurfaces $S$ in closed manifolds. For instance, if $S$ has non-vanishing mean curvature, we show its level set flow converges smoothly towards an embedded minimal…

Let M be a closed orientable irreducible 3-manifold, and let f be a diffeomorphism over M. We call an embedded 2-torus T an Anosov torus if it is invariant and the induced action of f over \pi_1(T) is hyperbolic. We prove that only few…

We prove an inequality for H\"older continuous differential forms on compact manifolds in which the integral of the form over the boundary of a sufficiently small, smoothly immersed disk is bounded by a certain multiplicative convex…

Motivated by non-equilibrium phenomena in nature, we study dynamical systems whose time-evolution is determined by non-stationary compositions of chaotic maps. The constituent maps are topologically transitive Anosov diffeomorphisms on a…

Let $M$ be a connected, closed, orientable, irreducible $3$-manifold. We show that: if $M$ admits a co-orientable taut foliation $\mathcal{F}$ with orderable cataclysm, then $\pi_1(M)$ is left orderable. This provides an elementary proof…

This paper shows any non-Anosov partially hyperbolic diffeomorphism on the 3-torus which is homotopic to Anosov must be accessible.

We consider a compact 3-dimensional boundaryless Riemannian manifold M and the set of divergence-free (or zero divergence) vector fields without singularities, then we prove that this set has a C1-residual such that any vector field inside…

Given a taut depth-one foliation $\mathcal{F}$ in a closed atoroidal 3-manifold $M$ transverse to a pseudo-Anosov flow $\phi$ without perfect fits, we show that the universal circle coming from leftmost sections $\mathfrak{S}_\mathrm{left}$…

Let $S_g$ be the closed surface of genus $g$, $\mathcal{L}$ be the infinite Jacob's ladder surface, and $\mathrm{Map}(S)$ denote the mapping class group of a surface $S$. Let $q_g:\mathcal{L}\to S_g$ be the regular infinite-sheeted cover…

The aim of this paper is to study dynamical and topological properties of a flow in the region of influence of an isolated non-saddle set or a $W$-set in a manifold. These are certain classes of compact invariant sets in whose vicinity the…

On a smooth compact Riemannian manifold without boundary, we construct a finite dimensional cohomological complex of currents that are invariant by an Axiom A flow verifying Smale's transversality assumptions. The cohomology of that complex…

We prove several rigidity results about the centralizer of a smooth diffeomorphism, concentrating on two families of examples: diffeomorphisms with transitive centralizer, and perturbations of isometric extensions of Anosov diffeomorphisms…

We show that any noncompact oriented surface is homeomorphic to the leaf of a minimal foliation of a closed $3$-manifold. These foliations are (or are covered by) suspensions of continuous minimal actions of surface groups on the circle.…

In this paper we focused our study on Derived From Anosov diffeomorphisms (DA diffeomorphisms ) of the torus $\mathbb{T}^3,$ it is, an absolute partially hyperbolic diffeomorphism on $\mathbb{T}^3$ homotopic to an Anosov linear automorphism…

We look at the properties of high frequency eigenmodes for the damped wave equation on a compact manifold with an Anosov geodesic flow. We study eigenmodes with spectral parameters which are asymptotically close enough to the real axis. We…