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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
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.
MSC classification
- Type
- Original Article
- Information
- Ergodic Theory and Dynamical Systems , Volume 42 , Issue 3: Anatole Katok Memorial Issue Part 2: Special Issue of Ergodic Theory and Dynamical Systems , March 2022 , pp. 1220 - 1251
- Copyright
- © The Author(s), 2021. Published by Cambridge University Press
References
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