Shear-shape cocycles for measured laminations and ergodic theory of the earthquake flow
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 earthquak...
Gespeichert in:
| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
24 August 2024
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| In: |
Geometry & topology
Year: 2024, Jahrgang: 28, Heft: 5, Pages: 1995-2124 |
| ISSN: | 1364-0380 |
| DOI: | 10.2140/gt.2024.28.1995 |
| Online-Zugang: | Verlag, kostenfrei, Volltext: https://doi.org/10.2140/gt.2024.28.1995 Verlag, kostenfrei, Volltext: https://msp.org/gt/2024/28-5/p01.xhtml 
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| Verfasserangaben: | Aaron Calderon, James Farre |
MARC
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| 520 | |a 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 upper-triangular subgroup P<SL2R 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. | ||
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