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hyperbolic orbifolds

Ergodic Theory and Dynamical Systems (1)

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Excursions to the cusps for geometrically finite hyperbolic orbifolds and equidistribution of closed geodesics in regular covers
Part of
- Ergodic theory
- Dynamical systems with hyperbolic behavior
RON MOR
Journal:

Ergodic Theory and Dynamical Systems / Volume 42 / Issue 12 / December 2022

Published online by Cambridge University Press:

15 November 2021, pp. 3745-3791

Print publication:

December 2022
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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.