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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 × 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 s and u on a Seifert manifold M . We show that if the foliation s or u contains a compact leaf, then the flow φ t is decomposed into a finite union of models which are defined on T 2 × 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...

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 , , ) of symplectic diffeomorphisms and Hamiltonian systems, exhibitinglargerobustly transitive sets. We show that the C 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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