Search results for "hyperbolicité"

showing 3 items of 3 documents

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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INSTABILITY OF HAMILTONIAN SYSTEMS IN THE SENSE OF CHIRIKOV AND BIFURCATION IN A NON LINEAR EVOLUTION PROBLEM EMANATING FROM PHYSICS

2004

We prove the existence of a minimal geometrico-dynamical condition to create hyperbolicity in section in the vicinity of a transversal homoclinic partially hyperbolic torus in a near integrable Hamiltonian system with three degrees of freedom. We deduce in this context a generalization of the Easton's theorem of symbolic dynamics. Then we give the optimal estimation of the Arnold diffusion time along a transition chain in the initially hyperbolic Hamiltonian systems with three degrees of freedom with a surrounding chain of hyperbolic periodic orbits .In a second part, we describe geometrically a mechanism of diffusion studied by Chirikov in a near integrable Hamiltonian system with three de…

[ MATH ] Mathematics [math]dynamique symboliquehyperbolicitymodulational instabilityNavier Stokespartially hyperbolic tori[MATH] Mathematics [math]amplitude equationschevauchement de résonancescenter manifoldconvection mixte –hyperbolicitéoverlapping resonancessymbolic dynamicséquations d'amplitudesystèmes Hamiltoniensbifurcationinstabilité modulationnellevariété centraleHamiltonian systems[MATH]Mathematics [math]tores partiellement hyperboliquesmixed convection
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