Integrable smooth planar billiards and evolutes.
Invariant Measures and Minimal Sets of Horospherical Flows.
Invariant measures for the stable foliation on negatively curved periodic manifolds
We classify reversible measures for the stable foliation on manifolds which are infinite covers of compact negatively curved manifolds. We extend the known results from hyperbolic surfaces to varying curvature and to all dimensions.
Invariant measures of the geodesic flow and measures at infinity on negatively curved manifolds
Invariant two-forms for geodesic flows.
Khinchin type condition for translation surfaces and asymptotic laws for the Teichmüller flow
We study a diophantine property for translation surfaces, defined in terms of saddle connections and inspired by classical Khinchin condition. We prove that the same dichotomy holds as in Khinchin theorem, then we deduce a sharp estimate on how fast the typical Teichmüller geodesic wanders towards infinity in the moduli space of translation surfaces. Finally we prove some stronger result in genus one.
Labeled Rauzy classes and framed translation surfaces
In this paper, we compare two definitions of Rauzy classes. The first one was introduced by Rauzy and was in particular used by Veech to prove the ergodicity of the Teichmüller flow. The second one is more recent and uses a “labeling” of the underlying intervals, and was used in the proof of some recent major results about the Teichmüller flow.The Rauzy diagrams obtained from the second definition are coverings of the initial ones. In this paper, we give a formula that gives the degree of this covering.This...
Large deviations, Gibbs measures and closed orbits for hyperbolic flows.
Le flot géodésique des variétés riemanniennes à courbure négative
Lemme de l'ombre et non divergence des horosphères d'une variété géométriquement finie
Dans cet article, nous établissons dans un premier temps un lemme de l'ombre dans le cas des variétés géométriquement finies à courbure négative variable. Ce théorème donne des estimées très précises de la décroissance de la mesure de Patterson des ombres, sur le bord à l'infini de telles variétés. Nous en déduisons un résultat de non divergence des horosphères. Plus précisément, nous considérons certaines moyennes naturelles sur de grandes boules horosphériques, dont nous...
Lissajous knots and billiard knots
We show that Lissajous knots are equivalent to billiard knots in a cube. We consider also knots in general 3-dimensional billiard tables. We analyse symmetry of knots in billiard tables and show in particular that the Alexander polynomial of a Lissajous knot is a square modulo 2.
Magnetic flows and Gaussian thermostats on manifolds of negative curvature
We consider a class of flows which includes both magnetic flows and Gaussian thermostats of external fields. We give sufficient conditions for such flows on manifolds of negative sectional curvature to be Anosov.
Masse des pointes, temps de retour et enroulements en courbure négative
Soient un groupe discret géométriquement fini d’isométries d’une variété de Hadamard pincée et une pointe de l’orbifold associé . Munissant de sa mesure de Patterson-Sullivan , nous obtenons une estimation asymptotique de la masse d’un petit voisinage horocyclique de , moyennant une hypothèse sur la croissance du sous-groupe parabolique associé à , hypothèse qui est réalisée si est symétrique de rang . Nous en déduisons une estimation asymptotique du temps de retour du flot géodésique...
Mather measures and the Bowen–Series transformation
Metric with ergodic geodesic flow is completely determined by unparameterized geodesics.
Métriques à entropie topologique positive sur
Moduli spaces of abelian differentials : the principal boundary, counting problems, and the Siegel-Veech constants
A holomorphic 1-form on a compact Riemann surface S naturally defines a flat metric on S with cone-type singularities. We present the following surprising phenomenon: having found a geodesic segment (saddle connection) joining a pair of conical points one can find with a nonzero probability another saddle connection on S having the same direction and the same length as the initial one. A similar phenomenon is valid for the families of parallel closed geodesics. We give a complete description of...
Nonsingular cocycles and piecewise linear time changes.
On connections, geodesics and sprays in synthetic differential geometry
On the creation of conjugate points.