Related papers: Sub-actions for geodesic flows on locally CAT(-1) …

We provide a systematic coset construction of the effective field theories governing the low-energy dynamics of relativistic fluids and solids, and of their "super" counterparts. These effective theories agree with those previously derived…

We consider the geodesic flow of a compact connected rank 1 surface. We prove a formula for the topological pressure as the exponential growth rate of rank 1 periodic geodesics generalizing a previous result of K. Gelfert and B. Schapira…

We show that the geodesic flow and the exponential map of a $C^k$ submanifold of $\mathbb{R}^n$ with $k\geq 2$ are of class $C^{k-1}$.

We consider the volume preserving flow of smooth, closed and convex hypersurfaces in the hyperbolic space $\mathbb{H}^{n+1} (n\geq 2)$ with the speed given by arbitrary positive power $\alpha$ of the Gauss curvature. We prove that if the…

In this paper we describe the topological behavior of the geodesic flow for a class of closed 3-manifolds realized as quotients of nonstrictly convex Hilbert geometries, constructed and described explicitly by Benoist. These manifolds are…

Stationary flows of an inviscid and incompressible fluid of constant density in the region $D=(0, L)\times \mathbb R^2$, periodic in the second and third variables, are considered. The flux and the Bernoulli function are prescribed at each…

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 give a topological stability result for the action of the fundamental group of a compact manifold of negative curvature on its boundary at infinity: any nearby action of this group by homeomorphisms of the sphere is semi-conjugate to the…

In this thesis, we study the Teichm\"uller geodesic flow on the space of translation surfaces by introducing two related discrete-time dynamical systems. First, we discuss the Rauzy-Veech induction, highlighting its connections to interval…

We describe a family of arithmetic cross-sections for geodesic flow on compact surfaces of constant negative curvature based on the study of generalized Bowen-Series boundary maps associated to cocompact torsion-free Fuchsian groups and…

In this paper, an Alexandrov-Fenchel inequality is established for closed $2$-convex spacelike hypersurface in de Sitter space by investigating the behavior of the locally constrained inverse curvature flow \begin{align} \frac{\partial…

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…

We prove the integrability of geodesic flows on the Riemannian g.o. spaces of compact Lie groups, as well as on a related class of Riemannian homogeneous spaces having an additional principal bundle structure.

Let $M$ be a closed 3-manifold which admits an Anosov flow. In this paper we develop a technique for constructing partially hyperbolic representatives in many mapping classes of $M$. We apply this technique both in the setting of geodesic…

We localize the entropy functionals of G. Perelman and generalize his no-local-collapsing theorem and pseudo-locality theorem. Our generalization is technically inspired by further development of Li-Yau estimate along the Ricci flow. It can…

We prove some ergodic theorems for flat surfaces of finite area. The first result concerns such surfaces whose Teichmuller orbits are recurrent to a compact subset of $SL(2;R)/SL(S)$, where $SL(S)$ is the Veech group of the surface. In this…

Veech's Theorem claims that if $G$ is a locally compact\,(LC) Hausdorff topological group, then it may act freely on $G^{\textrm{LUC}}$. We prove Veech's Theorem for $G$ being only locally quasi-totally bounded, not necessarily LC. And we…

Given a closed Riemannian manifold, we prove the C0-general density theorem for continuous geodesic flows. More precisely, that there exists a residual (in the C0-sense) subset of the continuous geodesic flows such that, in that residual…

We introduce a notion of abelian cohomology in the context of smooth flows. This is an equivalence relation which is weaker than the standard cohomology equivalence relation for flows. We develop Livshits theory for abelian cohomology over…

We prove that the geodesic flow on closed surfaces displays a hyperbolic set if the shadowing property holds C2-robustly on the metric. Similar results are obtained when considering even feeble properties like the weak shadowing and the…