Pollicott, Mark (2017) Amenable covers for surfaces and growth of closed geodesics. Advances in Mathematics, 319 . pp. 599-609. doi:10.1016/j.aim.2017.08.020 ISSN 0001-8708.

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Abstract

In the study of surfaces and closed geodesics an important characteristic is the topological entropy.
Let M be a compact surface with a smooth Riemannian metric and denote by π(M, T) the number of closed geodesics of length at most T. A dynamical perspective comes from considering the geodesic flow φt: SM → SM on the three dimensional unit tangent bundle SM for M. For compact surfaces of negative curvature the topological entropy h(φ) of the associated geodesics flow corresponds to the growth rate of the number of closed geodesics π(M, T) with length at most T

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Surfaces , Topological entropy , Geodesics (Mathematics)
Journal or Publication Title:	Advances in Mathematics
Publisher:	Academic Press
ISSN:	0001-8708
Official Date:	15 October 2017
Dates:	Date Event 15 October 2017 Published 1 September 2017 Available 14 August 2017 Accepted
Volume:	319
Page Range:	pp. 599-609
DOI:	10.1016/j.aim.2017.08.020
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	3 October 2017
Date of first compliant Open Access:	1 September 2018

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