منابع مشابه
Lyapunov functions and Anosov flows
We show that if the codimension one Anosov flow Φ on a compact n-manifold M satisfies the so called condition (L), then there is a continuous Lyapunov function g : R → R, where R is the universal covering space of M , such that g strictly increases along the orbits of the lift of Φ and is constant on the leaves of the lift of the strong stable foliation of the “synchronization” (i.e. suitable r...
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We show that if a distribution is locally spanned by Lipschitz vector fields and is involutive a.e., then it is uniquely integrable giving rise to a Lipschitz foliation with leaves of class C1,Lip. As a consequence, we show that every codimension-one Anosov flow on a compact manifold of dimension > 3 such that the sum of its strong distributions is Lipschitz, admits a global cross section. The ...
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The study of decay of correlations for hyperbolic systems goes back to the work of Sinai [36] and Ruelle [32]. While a manifold of results were obtained thru the years for maps, some positive results have been established for Anosov flows only recently. Notwithstanding the proof of ergodicity, and mixing, for geodesic flows on manifolds of negative curvature [15, 1, 35] the first quantitative r...
متن کاملAnosov Flows of Codimension One
1995 The dissertation of Slobodan Simi c is approved, and is acceptable in quality and form for publication on microolm: Chair Date Date Date 1 Abstract Anosov Flows of Codimension One The main goal of this dissertation is to show the existence of global cross sections for certain classes of Anosov ows. Let be a C 2 codimension one Anosov ow on a compact Riemannian manifold M of dimension great...
متن کاملTight contact structures and Anosov flows
In this review, we demonstrate how classic and contemporary results on the classification of tight contact structures apply to the problem of existence and uniqueness of Anosov flows on three-manifolds. The ingredients we use are the results of Mitsumatsu on Anosov flows, the homotopy invariant of plane fields as described by Gompf and others, and certain recent classification results of Giroux...
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ژورنال
عنوان ژورنال: Topology
سال: 1972
ISSN: 0040-9383
DOI: 10.1016/0040-9383(72)90002-x