Pseudo orbit tracing property and fixed points
If a continuous map f of a compact metric space has the pseudo orbit tracing property and is h-expansive then the set of all fixed points of f is totally disconnected.
Puzzles of Quasi-Finite Type, Zeta Functions and Symbolic Dynamics for Multi-Dimensional Maps
Entropy-expanding transformations define a class of smooth dynamics generalizing interval maps with positive entropy and expanding maps. In this work, we build a symbolic representation of those dynamics in terms of puzzles (in Yoccoz’s sense), thus avoiding a connectedness condition, hard to satisfy in higher dimensions. Those puzzles are controled by a «constraint entropy» bounded by the hypersurface entropy of the aforementioned transformations.The analysis of those puzzles rests on a «stably...
Quantization of the orientation preserving automorphisms of the torus
Quasiconformality in the Geodesic Flow of Negatively Curved Manifolds.
Quasilinear waves and trapping: Kerr-de Sitter space
In these notes, we will describe recent work on globally solving quasilinear wave equations in the presence of trapped rays, on Kerr-de Sitter space, and obtaining the asymptotic behavior of solutions. For the associated linear problem without trapping, one would consider a global, non-elliptic, Fredholm framework; in the presence of trapping the same framework is available for spaces of growing functions only. In order to solve the quasilinear problem we thus combine these frameworks with the normally...
Quelques nouveaux invariants des difféomorphismes Morse--Smale d'une surface
Soit un difféomorphisme Morse-Smale d’une surface fermée. À une courbe instable de comportement 1 par rapport à un attracteur de correspond une courbe fermée sur un des tores (Bassin. Cette remarque nous permettra de définir de nouveaux invariants de conjugaison de . Nous en déduisons aussi un moyen d’écrire explicitement une puissance de comme le produit du temps 1 d’un champ de vecteurs Morse-Smale topologique par des isotopies à support des disques et des twists de Dehn de supports...
Quelques propriétés des lignes critiques d'une récurrence du second ordre à inverse non unique. Détermination d'une zone absorbante
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