Excursions to the cusps for geometrically finite hyperbolic orbifolds and equidistribution of closed geodesics in regular covers

We give a finitary criterion for the convergence of measures on non-elementary geometrically finite hyperbolic orbifolds to the unique measure of maximal entropy. We give an entropy criterion controlling escape of mass to the cusps of the orbifold. Using this criterion, we prove new results on the d...

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Bibliographic Details
Published inErgodic theory and dynamical systems Vol. 42; no. 12; pp. 3745 - 3791
Main Author MOR, RON
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.12.2022
Subjects
Criteria
Cusps
Entropy
Geodesy
Lie groups
Orbits
Original Article
closed geodesics
entropy
37D40
hyperbolic orbifolds
37A35
37A17
equidistribution
geometrically finite
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ISSN0143-3857
1469-4417
DOI10.1017/etds.2021.101

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Summary:We give a finitary criterion for the convergence of measures on non-elementary geometrically finite hyperbolic orbifolds to the unique measure of maximal entropy. We give an entropy criterion controlling escape of mass to the cusps of the orbifold. Using this criterion, we prove new results on the distribution of collections of closed geodesics on such an orbifold, and as a corollary, we prove the equidistribution of closed geodesics up to a certain length in amenable regular covers of geometrically finite orbifolds.
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ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2021.101