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

Part of: Dynamical systems with hyperbolic behavior Ergodic theory

Published online by Cambridge University Press:  15 November 2021

RON MOR Open the ORCID record for RON MOR [Opens in a new window]
RON MOR*
Affiliation:
The Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel
*
(e-mail: [email protected])
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Abstract

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.

Keywords

hyperbolic orbifoldsgeometrically finiteentropyclosed geodesicsequidistribution

MSC classification

Primary: 37A17: Homogeneous flows 37A35: Entropy and other invariants, isomorphism, classification 37D40: Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 42 , Issue 12 , December 2022 , pp. 3745 - 3791
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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