Search results for "hyperbolicité partielle"

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Chaotic dynamics and partial hyperbolicity

2017

The dynamics of hyperbolic systems is considered well understood from topological point of view as well as from stochastic point of view. S. Smale and R. Abraham gave an example showing that, in general, the hyperbolic systems are not dense among all differentiable systems. In 1970s, M. Brin and Y. Pesin proposed a new notion: partial hyperbolicity to release the notion of hyperbolicity. One aim of this thesis is to understand the dynamics of certain partially hyperbolic systems from stochastic point of view as well as from topological point of view. From stochastic point of view, we prove the following results: — There exists an open and dense subset U of robustly transitive nonhyperbolic …

Anosov flowPeriodic measureMesure périodiqueExposant de LyapunovTores transversaux[MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM]Homoclinic classTwist de DehnPartial hyperbolicityDehn twistMesure ergodique non hyperboliqueFlot d’AnosovNon-hyperbolic ergodic measureTransitivité robusteClasse homocliniqueRobust transitivityTransverse torusHyperbolicité partielleLyapunov exponent
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Partially hyperbolic diffeomorphisms with a compact center foliation with finite holonomy

2011

The thesis classifies partially hyperbolic diffeomorphisms with a compact center foliation with finite holonomy. Under the further assumption of a one-dimensional unstable bundle we show the following: If the unstable bundle is oriented then the system fibers over a hyperbolic toral automorphism. We further establish that the system has a dense orbit of center leaves. During the proof we show a Shadowing Lemma and the dynamical coherence without restrictions of the dimensions.

Mathematics::Dynamical Systems[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS][ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS]systèmes dynamiques[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]dynamical systemshyperbolicité partiellepartial hyperbolicitycompact foliationsfeuilletages compacts
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