Large group actions on manifolds.
Law of the Iterated Logarithm for Tranisitive C... Anosov Flows and Semiflows over Maps of the Interval.
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...
Linear actions of free groups
In this paper we study dynamical properties of linear actions by free groups via the induced action on projective space. This point of view allows us to introduce techniques from Thermodynamic Formalism. In particular, we obtain estimates on the growth of orbits and their limiting distribution on projective space.
Linear response for smooth deformations of generic nonuniformly hyperbolic unimodal maps
We consider families of unimodal maps whose critical point is slowly recurrent, and we show that the unique absolutely continuous invariant measure of depends differentiably on , as a distribution of order . The proof uses transfer operators on towers whose level boundaries are mollified via smooth cutoff functions, in order to avoid artificial discontinuities. We give a new representation of for a Benedicks-Carleson map , in terms of a single smooth function and the inverse branches...
Linearization of Normally Hyperbolic Diffeomorphisms and Flows
Links of homeomorphisms of a disk and topological entropy.
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.
Local density of diffeomorphisms with large centralizers
Given any compact manifold , we construct a non-empty open subset of the space of -diffeomorphisms and a dense subset such that the centralizer of every diffeomorphism in is uncountable, hence non-trivial.
Looking for the Bernoulli shift
Lorenz attractor through saddle-node bifurcations
Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
Lyapunov Exponents of Rank -Variations of Hodge Structures and Modular Embeddings
If the monodromy representation of a VHS over a hyperbolic curve stabilizes a rank two subspace, there is a single non-negative Lyapunov exponent associated with it. We derive an explicit formula using only the representation in the case when the monodromy is discrete.
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.
Maps of the interval Ljapunov stable on the set of nonwandering points.
Markov partitions for fibre expanding systems
Fibre expanding systems have been introduced by Denker and Gordin. Here we show the existence of a finite partition for such systems which is fibrewise a Markov partition. Such partitions have direct applications to the Abramov-Rokhlin formula for relative entropy and certain polynomial endomorphisms of ℂ².
Markov structures and decay of correlations for non-uniformly expanding dynamical systems
Markov structures for non-uniformly expanding maps on compact manifolds in arbitrary dimension.
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...