共查询到20条相似文献,搜索用时 15 毫秒
1.
Luchezar Stoyanov 《Comptes Rendus Mathematique》2013,351(17-18):669-672
We prove strong spectral estimates for Ruelle transfer operators for arbitrary contact Anosov flows. As a consequence of this we obtain: (a) existence of a non-zero analytic continuation of the Ruelle zeta function with a pole at the entropy in a vertical strip containing the entropy in its interior; (b) a Prime Orbit Theorem with an exponentially small error; (c) exponential decay of correlations for Hölder continuous observables with respect to any Gibbs measure. 相似文献
2.
Domenico Perrone 《Journal of Geometry》2005,83(1-2):164-174
We prove that on a compact (non Sasakian) contact metric 3-manifold with critical metric for the Chern-Hamilton functional,
the characteristic vector field ξ is conformally Anosov and there exists a smooth curve in the contact distribution of conformally
Anosov flows. As a consequence, we show that negativity of the ξ-sectional curvature is not a necessary condition for conformal
Anosovicity of ξ (this completes a result of [4]). Moreover, we study contact metric 3-manifolds with constant ξ-sectional
curvature and, in particular, correct a result of [13]. 相似文献
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S. R. Fenley 《Commentarii Mathematici Helvetici》1998,73(2):259-297
In this article we study the topology of Anosov flows in 3-manifolds. Specifically we consider the lifts to the universal
cover of the stable and unstable foliations and analyze the leaf spaces of these foliations. We completely determine the structure
of the non Hausdorff points in these leaf spaces. There are many consequences: (1) when the leaf spaces are non Hausdorff,
there are closed orbits in the manifold which are freely homotopic, (2) suspension Anosov flows are, up to topological conjugacy,
the only Anosov flows without free homotopies between closed orbits, (3) when there are infinitely many stable leaves (in
the universal cover) which are non separated from each other, then we produce a torus in the manifold which is transverse
to the Anosov flow and therefore is incompressible, (4) we produce non Hausdorff examples in hyperbolic manifolds and derive
important properties of the limit sets of the stable/unstable leaves in the universal cover.
Received: March 13, 1997 相似文献
5.
Slobodan Simic 《Proceedings of the American Mathematical Society》1996,124(6):1869-1877
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 . As a consequence, we show that every codimension-one Anosov flow on a compact manifold of dimension such that the sum of its strong distributions is Lipschitz, admits a global cross section.
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Yong Fang 《Comptes Rendus Mathematique》2003,336(5):419-422
We show that for a smooth Anosov flow on a closed five dimensional manifold, if it has C∞ Anosov splitting and preserves a C∞ pseudo-Riemannian metric, then up to a special time change and finite covers, it is C∞ flow equivalent either to the suspension of a symplectic hyperbolic automorphism of , or to the geodesic flow on a three dimensional hyperbolic manifold. To cite this article: Y. Fang, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
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David Fried 《Topology》1983,22(3):299-303
ATRANSITIVEAnosov flow on a closed manifold Mis one with the qualitative behavior of a geodesic flow on a surface of negative curvature, that is global hyperbelocity and dense periodic set. A psedo-Anosov map is a homeomorphism of closed surface that has finitely many prescribed prong singlarities and is smooth and hyperbolic elsewhere: we refer to the Orsay Thurston Seminar for details [2]. We will show that Birkhoff's surfaces of section[1] can be used to established a close connection between these systems then M has dimension 3. This extends the srgery techniques of [4,5] to produce all the transitive Anove flows in dimension 3. 相似文献
10.
Pierre Dehornoy 《Comptes Rendus Mathematique》2013,351(3-4):127-129
Two flows are almost commensurable if, up to removing finitely many periodic orbits and taking finite coverings, they are topologically equivalent. We prove that all suspensions of automorphisms of the 2-dimensional torus and all geodesic flows on unit tangent bundles to hyperbolic 2-orbifolds are pairwise almost commensurable. 相似文献
11.
David Ruelle 《Inventiones Mathematicae》1976,34(3):231-242
Given a real-analytic expanding endomorphism of a compact manifoldM, a meromorphic zeta function is defined on the complex-valued real-analytic functions onM. A zeta function for Anosov flows is shown to be meromorphic if the flow and its stable-unstable foliations are real-analytic. 相似文献
12.
M. Ratner 《Israel Journal of Mathematics》1974,17(4):380-391
We consider a special flowS
t over a shift in the space of sequences (X, μ) constructed using a continuousf with {fx380-1}
We formulate a condition for μ such that theK-flowS
t is aB-flow.
A note on the paperGeodesic flows are Bernoullian by D. Ornstein and B. Weiss. 相似文献
13.
Masayuki Asaoka 《Inventiones Mathematicae》2008,174(2):435-462
We show that any topologically transitive codimension-one Anosov flow on a closed manifold is topologically equivalent to
a smooth Anosov flow that preserves a smooth volume. By a classical theorem due to Verjovsky, any higher-dimensional codimension-one
Anosov flow is topologically transitive. Recently, Simić showed that any higher-dimensional codimension-one Anosov flow that
preserves a smooth volume is topologically equivalent to the suspension of an Anosov diffeomorphism. Therefore, our result
gives a complete classification of codimension-one Anosov flows up to topological equivalence in higher dimensions. 相似文献
14.
Yong Fang 《Geometriae Dedicata》2010,145(1):139-150
Let g be a negatively curved Riemannian metric of a closed C
∞ manifold M of dimension at least three. Let L
λ be a C
∞ one-parameter convex superlinear Lagrangian on TM such that
L0(v) = \frac12 g(v, v){L_0(v)= \frac{1}{2} g(v, v)} for any v ∈ TM. We denote by jl{\varphi^\lambda} the restriction of the Euler-Lagrange flow of L
λ on the
\frac12{\frac{1}{2}} -energy level. If λ is small enough then the flow jl{\varphi^\lambda} is Anosov. In this paper we study the geometric consequences of different assumptions about the regularity of the Anosov
distributions of jl{\varphi^\lambda} . For example, in the case that the initial Riemannian metric g is real hyperbolic, we prove that for λ small, jl{\varphi^\lambda} has C
3 weak stable and weak unstable distributions if and only if jl{\varphi^\lambda} is C
∞ orbit equivalent to the geodesic flow of g. 相似文献
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Supported in part by grants from the NSF and the Sloan Foundation. 相似文献
17.
Masayuki Asaoka 《Topology and its Applications》2007,154(7):1263-1268
We show that if a C2 codimension one foliation on a three-dimensional manifold has a Reeb component and is invariant under a projectively Anosov flow, then it must be a Reeb foliation on S2×S1. 相似文献
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