Shear-shape cocycles for measured laminations and ergodic theory of the earthquake flow
arXiv:2102.13124 · doi:10.2140/gt.2024.28.1995
Abstract
We extend Mirzakhani's conjugacy between the earthquake and horocycle flows to a bijection, demonstrating conjugacies between these flows on all strata and exhibiting an abundance of new ergodic measures for the earthquake flow. The structure of our map indicates a natural extension of the earthquake flow to an action of the the upper-triangular subgroup P < SL(2,R) and we classify the ergodic measures for this action as pullbacks of affine measures on the bundle of quadratic differentials. Our main tool is a generalization of the shear coordinates of Bonahon and Thurston to arbitrary measured laminations.
90 pages, 29 figures. Final version, to appear in G&T
References in corpus (6)
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- Limits of geodesic push-forwards of horocycle invariant measures
- Length statistics of random multicurves on closed hyperbolic surfaces
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