Related papers: Genus one Birkhoff sections for geodesic flows

We study totally geodesic codimension 1 smooth foliations on Lorentzian manifold. We are in particular interested by the relations between riemannian flows and geodesic foliations. We prove that, up to a 2-cover, any Seifert bundle admit…

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.

In this paper, we study transversely holomorphic partially hyperbolic flows, i.e. those whose holonomy pseudo-group is given by biholomorphic maps. We prove in the seven-dimensional case that under the assumption that the subcenter…

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 $C^{k-1}$.

If $(M,g)$ is a smooth compact rank $1$ Riemannian manifold without focal points, it is shown that the measure $\mu_{\max}$ of maximal entropy for the geodesic flow is unique. In this article, we study the statistic properties and prove…

In this paper we use broken book decompositions to study Reeb flows on closed $3$-manifolds. We show that if the Liouville measure of a nondegenerate contact form can be approximated by periodic orbits, then there is a Birkhoff section for…

We construct geometrically infinite hyperbolic surfaces supporting horocycles with tailored recurrence properties. In particular, we obtain the first examples of non-trivial minimal horocyclic orbit closures and of infinite locally-finite…

In this paper we study topological aspects of the dynamics of the foliated horocycle flow on flat projective bundles over hyperbolic surfaces and we derive ergodic consequences. If $\rho : \Gamma \to {\rm PSL}(n+1,\mathbb{R})$ is a…

We give a natural definition of geodesics on a Riemannian supermanifold and extend the usual geodesic flow defined on the cotangent bundle of the body of the supermanifold, associated to the induced Riemannian structure on the body, to a…

In this paper, we study the Birkhoff sections in a 3-manifold foliated by invariant tori. We establish the necessary and sufficient conditions for various types of periodic orbits to serve as boundary orbits of a Birkhoff section. The…

We describe all possible topological structures of typical one-parameter bifurcations of gradient flows on the 2-sphere with holes in the case that the number of singular point of flows is at most six. To describe structures, we separatrix…

Let M be a non-elementary convex cocompact hyperbolic 3 manifold and delta the critical exponent of its fundamental group. We prove that a one-dimensional unipotent flow for the frame bundle of M is ergodic for the Burger-Roblin measure…

We calculate the local Riemann-Roch numbers of the zero sections of $T^*S^n$ and $T^*\R P^n$, where the local Riemann-Roch numbers are defined by using the $S^1$-bundle structure on their complements associated to the geodesic flows.

We use a result of J. Mather on the existence of connecting orbits for compositions of monotone twist maps of the cylinder to prove the existence of connecting geodesics on the unit tangent bundle $ST^2$ of the 2-torus in regions without…

A geometric characterization of the structure of the group of automorphisms of an arbitrary Birkhoff-Grothendieck bundle splitting $\bigoplus_{i=1}^{r} \mathcal(m_{i})$ over $\mathbb{C}\mathbb{P}^{1}$ is provided, in terms of its action on…

We associate to a CAT(0)-space a flow space that can be used as the replacement for the geodesic flow on the sphere tangent bundle of a Riemannian manifold. We use this flow space to prove that CAT(0)-group are transfer reducible over the…

We prove a quantitative version of the non-uniform hyperbolicity of the Teichm\"uller geodesic flow. Namely, at each point of any Teichm\"uller flow line, we bound the infinitesimal spectral gap for variations of the Hodge norm along the…

We show exactly which Seifert manifolds support partially hyperbolic dynamical systems. In particular, a circle bundle over a higher-genus surface supports a partially hyperbolic system if and only if it supports an Anosov flow. We also…

A sectional-Anosov flow on a manifold M is a C^1 vector field inwardly transverse to the boundary for which the maximal invariant is sectional-hyperbolic. We prove that every attractor of every vector field C^1 close to a transitive…

We study magnetic geodesic flows invariant under rotations on the 2-sphere. The dynamical system is given by a generic pair of functions $(f,\Lambda)$ in one variable. Topology of the Liouville fibration of the given integrable system near…