相关论文: Dynamical torsion for contact Anosov flows

Given a $\vartheta$-Anosov representation into a real reductive group $G$, we construct a natural resonance spectrum associated with the representation. This spectrum is a complex analytic variety of codimension $1$ in…

We adapt to $C^r$ Anosov flows on compact manifolds a construction for $C^r$ discrete-time hyperbolic dynamics ($r>1$), obtaining anisotropic Banach or Hilbert spaces on which the resolvent of the generator of weighted transfer operators…

Using bi-contact geometry, we define a new type of Dehn surgery on an Anosov flow with orientable weak invariant foliations. The Anosovity of the new flow is strictly connected to contact geometry and the Reeb dynamics of the defining…

A complete description of resonances for rational toral Anosov diffeomorphisms preserving certain Reinhardt domains is presented. As a consequence it is shown that every homotopy class of two-dimensional Anosov diffeomorphisms contains maps…

In this paper we present a proof of the Verjovsky conjecture: Every codimension-one Anosov flow on a manifold of dimension greater than three is topologically equivalent to the suspension of a hyperbolic toral automorphism. In fact, the…

We prove that divergent, extended geometrically finite (in the sense of Weisman arXiv:2205.07183) representations can be interpreted as restricted Anosov (in the sense of Tholozan--Wang arXiv:2307.02934) representations over certain flow…

Many natural real-valued functions of closed curves are known to extend continuously to the larger space of geodesic currents. For instance, the extension of length with respect to a fixed hyperbolic metric was a motivating example for the…

We define and study the foliated centralizer: the group of $C^\infty$ centralizer elements of the lift of an Anosov system on a non-compact manifold which additionally preserve the stable and unstable foliations. When the Anosov system is…

We provide a 3 dimensional contact geometric characterization of Anosov 3-flows based on interactions with Reeb dynamics. We investigate basic properties of the space of the resulting geometries and in particular show that such space is…

We show that if a hyperbolic 3-manifold admits a partially hyperbolic diffeomorphism then it also admits an Anosov flow. Moreover, we give a complete classification of partially hyperbolic diffeomorphism in hyperbolic 3-manifolds as well as…

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…

We study $3$-dimensional partially hyperbolic diffeomorphisms that are homotopic to the identity, focusing on the geometry and dynamics of Burago and Ivanov's center stable and center unstable \emph{branching} foliations. This extends our…

We prove that the twisted De Rham cohomology of a flat vector bundleover some smooth manifold is isomorphic to the cohomology of invariant Pollicott--Ruelleresonant states associated with Anosov and Morse--Smale flows. As a consequence,…

We show, using semiclassical measures and unstable derivatives, that a smooth vector field $X$ generating a contact Anosov flow on a $3$-dimensional manifold $\mathcal{M}$ has only finitely many Ruelle resonances in the vertical strips $\{…

A long-standing conjecture in Hamiltonian Dynamics states that the Reeb flow of any convex hypersurface in $\mathbb{R}^{2n}$ carries an elliptic closed orbit. Two important contributions toward its proof were given by Ekeland in 1986 and…

We prove that every sectional Anosov flow (or, equivalently, every sectional-hyperbolic attracting set of a flow) on a compact manifold has a periodic orbit. This extends the previous three-dimensional result obtained in [Existence of…

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 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…

In this paper, we prove Ruelle's inequality for the geodesic flow in non-compact manifolds with Anosov geodesic flow and some assumptions on the curvature. In the same way, we obtain Pesin's formula for Anosov geodesic flow in non-compact…

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,…