Shear-shape cocycles for measured laminations and ergodic theory of the earthquake flow
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866929482731880448 |
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| author | Calderon, Aaron Farre, James |
| author_facet | Calderon, Aaron Farre, James |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_13124 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Shear-shape cocycles for measured laminations and ergodic theory of the earthquake flow Calderon, Aaron Farre, James Geometric Topology Dynamical Systems 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. |
| title | Shear-shape cocycles for measured laminations and ergodic theory of the earthquake flow |
| topic | Geometric Topology Dynamical Systems |
| url | https://arxiv.org/abs/2102.13124 |