منابع مشابه
On the Topologically Conjugate Classes of Anosov Endomorphisms on Tori
This paper considers the following question: Given an Anosov endomorphism f on T, whether f is topologically conjugate to some hyperbolic toral endomorphism? It is well known that the answer for Anosov diffeomorphisms and expanding endomorphisms is affirmative. However, for the remainder Anosov endomorphisms, a quite different answer is obtained in this paper, i.e., for generic Anosov endomorph...
متن کاملSimplicial Endomorphisms
A presentation by generators and relations is given for the monoids of endomorphisms in the simplicial category. These monoids are submonoids of monoids one finds in Temperley-Lieb algebras, and as the monoids of Temperley-Lieb algebras are linked to situations where an endofunctor is adjoint to itself, so the monoids of simplicial endomorphisms axiomatized here are linked to arbitrary adjoint ...
متن کاملStability of Anosov Diffeomorphisms
Definition 1. Let < , > be a C∞ Riemannian metric on M and | · | its induced norm on TxM for each x ∈ M . We say that f ∈ D is Anosov if 1. the tangent bundle of M splits in a Whitney direct sum of continuous subbundles TM = E ⊕ E, where E and E are Df -invariant, 2. there exists constants c, c′ > 0 and 0 < λ < 1 such that |Dfn xv| < c λn|v| |Df−n x w| < c′ λn|w| for all x ∈ M , v ∈ E x, and w ...
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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 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...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 1976
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-58-3-249-285