Stable Ergodicity and Frame Flows

Keith Burns; Mark Pollicott

doi:10.1023/A:1024057924334

Stable Ergodicity and Frame Flows

Keith Burns^*, Mark Pollicott

^*Corresponding author for this work

Mathematics

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

9 Scopus citations

Abstract

In this note we show that all diffeomorphisms close enough to the time-one map of the frame flow on certain negatively curved manifolds are ergodic. As a simple corollary we deduce that the frame flows are ergodic for all compact manifolds with curvature pinched sufficiently close to -1, thus providing results in the case of manifolds of dimension 7 or 8 which were missing from the results of Brin and Karcher.

Original language	English (US)
Pages (from-to)	189-210
Number of pages	22
Journal	Geometriae Dedicata
Volume	98
Issue number	1
DOIs	https://doi.org/10.1023/A:1024057924334
State	Published - Apr 2003

Keywords

Frame flow
Partial hyperbolicity
Stable ergodicity

ASJC Scopus subject areas

Geometry and Topology

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10.1023/A:1024057924334

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AB - In this note we show that all diffeomorphisms close enough to the time-one map of the frame flow on certain negatively curved manifolds are ergodic. As a simple corollary we deduce that the frame flows are ergodic for all compact manifolds with curvature pinched sufficiently close to -1, thus providing results in the case of manifolds of dimension 7 or 8 which were missing from the results of Brin and Karcher.

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KW - Partial hyperbolicity

KW - Stable ergodicity

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Stable Ergodicity and Frame Flows

Abstract

Keywords

ASJC Scopus subject areas

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