Hyperbolic behaviour of geodesic flows on manifolds with no focal points

Keith Burns

doi:10.1017/S0143385700001796

Hyperbolic behaviour of geodesic flows on manifolds with no focal points

Keith Burns^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

It is shown that the unit tangent bundle of a compact uniform visibility manifold with no focal points contains a subset of positive Liouville measure on which all the characteristic exponents of the geodesic flow (except in the flow direction) are non-zero. This completes Pesin's proof that the geodesic flow of such a manifold is Bernoulli.

Original language	English (US)
Pages (from-to)	1-12
Number of pages	12
Journal	Ergodic Theory and Dynamical Systems
Volume	3
Issue number	1
DOIs	https://doi.org/10.1017/S0143385700001796
State	Published - Mar 1983

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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title = "Hyperbolic behaviour of geodesic flows on manifolds with no focal points",

abstract = "It is shown that the unit tangent bundle of a compact uniform visibility manifold with no focal points contains a subset of positive Liouville measure on which all the characteristic exponents of the geodesic flow (except in the flow direction) are non-zero. This completes Pesin's proof that the geodesic flow of such a manifold is Bernoulli.",

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AB - It is shown that the unit tangent bundle of a compact uniform visibility manifold with no focal points contains a subset of positive Liouville measure on which all the characteristic exponents of the geodesic flow (except in the flow direction) are non-zero. This completes Pesin's proof that the geodesic flow of such a manifold is Bernoulli.

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Hyperbolic behaviour of geodesic flows on manifolds with no focal points

Abstract

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