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Conformal Geometry and Dynamics

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


Author: Ser-Wei Fu
Journal: Conform. Geom. Dyn. 23 (2019), 251-261
MSC (2010): Primary 37D40, 53A35
DOI: https://doi.org/10.1090/ecgd/344
Published electronically: November 20, 2019
MathSciNet review: 4033067
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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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Additional Information

Ser-Wei Fu
Affiliation: National Center for Theoretical Sciences, No. 1 Sec. 4 Roosevelt Road, National Taiwan University, Taipei, 106, Taiwan
Email: swfu@ncts.ntu.edu.tw

DOI: https://doi.org/10.1090/ecgd/344
Received by editor(s): December 21, 2016
Received by editor(s) in revised form: March 19, 2019, and September 11, 2019
Published electronically: November 20, 2019
Article copyright: © Copyright 2019 American Mathematical Society