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Nous présentons plusieurs résultats de rigidité concernant les flots d’Anosov admettant transversalement des structures symplectiques réelles ou complexes de dimension $5$ .

Récurrence des marches aléatoires et ergodicité du flot géodésique sur les graphes réguliers.

M. Coornaert, A. Papadoppoulos (1996)

Mathematica Scandinavica

Recurrent point set of the shift on Σ and strong chaos

Lidong Wang, Gongfu Liao, Yu Yang (2002)

Annales Polonici Mathematici

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

Masayuki Asaoka (2010)

Annales de l’institut Fourier

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 $T^{2} \times I$ -models. We also apply our method to rigidity problems of some group actions.

Regular projectively Anosov flows with compact leaves

Takeo Noda (2004)

Annales de l’institut Fourier

This paper concerns projectively Anosov flows $φ^{t}$ with smooth stable and unstable foliations $ℱ^{s}$ and $ℱ^{u}$ on a Seifert manifold $M$ . We show that if the foliation $ℱ^{s}$ or $ℱ^{u}$ contains a compact leaf, then the flow $φ^{t}$ is decomposed into a finite union of models which are defined on $T^{2} \times I$ and bounded by compact leaves, and therefore the manifold $M$ 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.

Chernov, N. (2006)

Mathematical Physics Electronic Journal [electronic only]

Regularity of measure theoretic entropy for geodesic flows of negative curvature: I.

Gerhard Knieper, Howard Weiss (1989)

Inventiones mathematicae

Regularity of topological and metric entropy of hyperbolic flows.

Gonzalo Contreras (1992)

Mathematische Zeitschrift

Representations of the Whitehead manifold $W h^{3}$ and Julia sets

Valentin Poénaru, Corrado Tanasi (1995)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Return time statistics for unimodal maps

H. Bruin, S. Vaienti (2003)

Fundamenta Mathematicae

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.

Gallavotti, Giovanni (1995)

Mathematical Physics Electronic Journal [electronic only]

Rigid reparametrizations and cohomology for horocycle flows.

M. Ratner (1987)

Inventiones mathematicae

Rigidité différentiable des groupes fuchsiens

Étienne Ghys (1993)

Publications Mathématiques de l'IHÉS

Rigidité du flot géodésique de certaines nilvariétés de rang deux

Hamid-Reza Fanaï (1996/1997)

Séminaire de théorie spectrale et géométrie

Robust controller design for modified projective synchronization of Chen-Lee chaotic systems with nonlinear inputs.

Lin, Jui-Sheng, Pai, Neng-Sheng, Yau, Her-Terng (2009)

Mathematical Problems in Engineering

Robust transitivity in hamiltonian dynamics

Meysam Nassiri, Enrique R. Pujals (2012)

Annales scientifiques de l'École Normale Supérieure

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 $C^{r}$ open sets ( $r = 1, 2, \dots, \infty$ ) of symplectic diffeomorphisms and Hamiltonian systems, exhibitinglargerobustly transitive sets. We show that the $C^{\infty}$ 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...

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