Cusp excursions for the earthquake flow on the once-punctured torus
Geometric Topology
2019-03-20 v4
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.
Cite
@article{arxiv.1506.04534,
title = {Cusp excursions for the earthquake flow on the once-punctured torus},
author = {Ser-Wei Fu},
journal= {arXiv preprint arXiv:1506.04534},
year = {2019}
}
Comments
11 pages, 2 figures, edited main theorem and added corollary. Updated according to referee's comments