Resonances for Axiom ${\bf A}$ flows
نویسندگان
چکیده
منابع مشابه
Axiom a Flows with a Transverse Torus
Let X be an Axiom A flow with a transverse torus T exhibiting a unique orbit O that does not intersect T . Suppose that there is no nullhomotopic closed curve in T contained in either the stable or unstable set of O. Then we show that X has either an attracting periodic orbit or a repelling periodic orbit or is transitive. In particular, an Anosov flow with a transverse torus is transitive if i...
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In the paper, we prove convergence of moments of all orders for Axiom A diffeomorphisms and flows. The same results hold for nonuniformly hyperbolic diffeomorphisms and flows modelled by Young towers with superpolynomial tails. For polynomial tails, we prove convergence of moments up to a certain order, and give examples where moments diverge when this order is exceeded. Nonuniformly hyperbolic...
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Indeed, Margulis [lo] announced that for the geodesic flow on a d-dimensional compact manifold of curvature 1 the number of periodic orbits 7 with (minimal) period r(1) I x is asymptotic to ecd-‘jx/(d 1)x. This result bears a striking resemblance to the prime number theorem. Parry and Pollicott [12], following earlier work by Bowen [2, 41, generalized Margulis’ theorem to weakly mixing Axiom A ...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 1987
ISSN: 0022-040X
DOI: 10.4310/jdg/1214440726