Random dynamics and its applications.
Random mappings with a single absorbing center and combinatorics of discretizations of the logistic mapping.
Random perturbations and statistical properties of Hénon-like maps
Real analytic convex surfaces with positive topological entropy and rigid body dynamics.
Real and complex transversely symplectic Anosov flows of dimension five
Nous présentons plusieurs résultats de rigidité concernant les flots d’Anosov admettant transversalement des structures symplectiques réelles ou complexes de dimension .
Récurrence des marches aléatoires et ergodicité du flot géodésique sur les graphes réguliers.
Recurrent point set of the shift on Σ and strong chaos
Let (Σ,ϱ) be the one-sided symbolic space (with two symbols), and let σ be the shift on Σ. We use A(·), R(·) to denote the set of almost periodic points and the set of recurrent points respectively. In this paper, we prove that the one-sided shift is strongly chaotic (in the sense of Schweizer-Smítal) and there is a strongly chaotic set 𝒥 satisfying 𝒥 ⊂ R(σ)-A(σ).
Regular projectively Anosov flows on three-dimensional manifolds
We give the complete classification of regular projectively Anosov flows on closed three-dimensional manifolds. More precisely, we show that such a flow must be either an Anosov flow or decomposed into a finite union of -models. We also apply our method to rigidity problems of some group actions.
Regular projectively Anosov flows with compact leaves
This paper concerns projectively Anosov flows with smooth stable and unstable foliations and on a Seifert manifold . We show that if the foliation or contains a compact leaf, then the flow is decomposed into a finite union of models which are defined on and bounded by compact leaves, and therefore the manifold is homeomorphic to the 3-torus. In the proof, we also obtain a theorem which classifies codimension one foliations on Seifert manifolds with compact leaves which are incompressible...
Regularity of local manifolds in dispersing billiards.
Regularity of measure theoretic entropy for geodesic flows of negative curvature: I.
Regularity of topological and metric entropy of hyperbolic flows.
Representations of the Whitehead manifold and Julia sets
Return time statistics for unimodal maps
We prove that a non-flat S-unimodal map satisfying a weak summability condition has exponential return time statistics on intervals around a.e. point. Moreover we prove that the convergence to the entropy in the Ornstein-Weiss formula enjoys normal fluctuations.
Reversible Anosov diffeomorphisms and large deviations.
Rigid reparametrizations and cohomology for horocycle flows.
Rigidité différentiable des groupes fuchsiens
Rigidité du flot géodésique de certaines nilvariétés de rang deux
Robust controller design for modified projective synchronization of Chen-Lee chaotic systems with nonlinear inputs.
Robust transitivity in hamiltonian dynamics
A goal of this work is to study the dynamics in the complement of KAM tori with focus on non-local robust transitivity. We introduce open sets () of symplectic diffeomorphisms and Hamiltonian systems, exhibitinglargerobustly transitive sets. We show that the closure of such open sets contains a variety of systems, including so-calleda priori unstable integrable systems. In addition, the existence of ergodic measures with large support is obtained for all those systems. A main ingredient of...