منابع مشابه
On Contact Anosov Flows
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 کاملLyapunov 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...
متن کاملLipschitz Distributions and Anosov Flows
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 ...
متن کاملA Local Trace Formula for Anosov Flows
We prove a local trace formula for Anosov flows. It relates Pollicott–Ruelle resonances to the periods of closed orbits. As an application, we show that the counting function for resonances in a sufficiently wide strip cannot have a sublinear growth. In particular, for any Anosov flow there exist strips with infinitely many resonances.
متن کاملOseledets Regularity Functions for Anosov Flows
Oseledets regularity functions quantify the deviation between the growth associated with a dynamical system along its Lyapunov bundles and the corresponding uniform exponential growth. Precise degree of regularity of these functions is unknown. We show that for every invariant Lyapunov bundle of a volume preserving Anosov flow on a closed smooth Riemannian manifold, the corresponding Oseledets ...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2015
ISSN: 0143-3857,1469-4417
DOI: 10.1017/etds.2015.25