Cusp excursions for the earthquake flow on the once-punctured torus

Fu, Ser-Wei

doi:10.1090/ecgd/344

Cusp excursions for the earthquake flow on the once-punctured torus
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by Ser-Wei Fu

Conform. Geom. Dyn. 23 (2019), 251-261

DOI: https://doi.org/10.1090/ecgd/344

Published electronically: November 20, 2019

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Abstract:

In this paper we study the typical speed of a generic earthquake trajectory leaving compact sets in the moduli space of the once-punctured torus. Mirzakhani showed that the earthquake flow is measurably equivalent to the horocyclic flow, which has been studied extensively. Our main result shows that the earthquake flow and the horocyclic flow behave very differently in cusp excursions. In particular, we prove a relation between the systole function and continued fractions and discuss the cusp excursions of earthquake trajectories.

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