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Anosov flows, growth rates on covers and group extensions of subshifts
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Dougall, Rhiannon and Sharp, Richard (2021) Anosov flows, growth rates on covers and group extensions of subshifts. Inventiones Mathematicae, 223 . pp. 445-483. doi:10.1007/s00222-020-00994-3 ISSN 0020-9910.
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Official URL: https://doi.org/10.1007/s00222-020-00994-3
Abstract
The aim of this paper is to study growth properties of group extensions of hyperbolic dynamical systems, where we do not assume that the extension satisfies the symmetry conditions seen, for example, in the work of Stadlbauer on symmetric group extensions and of the authors on geodesic flows. Our main application is to growth rates of periodic orbits for covers of an Anosov flow: we reduce the problem of counting periodic orbits in an amenable cover X to counting in a maximal abelian subcover Xab. In this way, we obtain an equivalence for the Gurevič entropy: h(X)=h(Xab) if and only if the covering group is amenable. In addition, when we project the periodic orbits for amenable covers X to the compact factor M, they equidistribute with respect to a natural equilibrium measure — in the case of the geodesic flow, the measure of maximal entropy.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Anosov flows, Hyperbolic groups , Symmetry groups , Geodesic flows | ||||||||
Journal or Publication Title: | Inventiones Mathematicae | ||||||||
Publisher: | Springer | ||||||||
ISSN: | 0020-9910 | ||||||||
Official Date: | 2021 | ||||||||
Dates: |
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Volume: | 223 | ||||||||
Page Range: | pp. 445-483 | ||||||||
DOI: | 10.1007/s00222-020-00994-3 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 25 August 2020 | ||||||||
Date of first compliant Open Access: | 27 August 2020 | ||||||||
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