Incompressibility of tori transverse to Axiom A flows
نویسندگان
چکیده
منابع مشابه
Incompressibility of Tori Transverse to Axiom a Flows
We prove that a torus transverse to an Axiom A vector field that does not exhibit sinks, sources or null homotopic periodic orbits on a closed irreducible 3-manifold is incompressible. This strengthens the works of Brunella (1993), Fenley (1995), and Mosher (1992).
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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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Let p be a prime integer, F a field of characteristic not p, T the norm torus of a degree p extension field of F , and E a T -torsor over F such that the degree of each closed point on E is divisible by p (a generic T -torsor has this property). We prove that E is p-incompressible. Moreover, all smooth compactifications of E (including those given by toric varieties) are p-incompressible. The m...
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We develop the multifractal analysis of conformal axiom A flows. This includes the study of the Hausdorff dimension of basic sets of the flow, the description of the dimension spectra for pointwise dimension and for Lyapunov exponents and the multifractal decomposition associated with these spectra. The main tool of study is the thermodynamic formalism for hyperbolic flows by Bowen and Ruelle. ...
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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: Proceedings of the American Mathematical Society
سال: 2008
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-08-09409-4