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Counting closed geodesics in a compact rank-one locally CAT(0) space

Published online by Cambridge University Press:  27 August 2021

RUSSELL RICKS*
Affiliation:
Binghamton University, Binghamton, New York, USA

Abstract

Let X be a compact, geodesically complete, locally CAT(0) space such that the universal cover admits a rank-one axis. Assume X is not homothetic to a metric graph with integer edge lengths. Let $P_t$ be the number of parallel classes of oriented closed geodesics of length at most t; then $\lim \nolimits _{t \to \infty } P_t / ({e^{ht}}/{ht}) = 1$ , where h is the entropy of the geodesic flow on the space $GX$ of parametrized unit-speed geodesics in X.

Type
Original Article
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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