Hamiltonian flows for pseudo-Anosov mapping classes
For a given pseudo-Anosov homeomorphism q) of a closed surface S, the action of q) on the Teichmuller space T (S) preserves the Weil-Petersson symplectic form. We give explicit formulae for two invariant functions T (S) R whose symplectic gradients generate autonomous Hamiltonian flows that coincide...
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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
24 May 2023
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| In: |
Commentarii mathematici Helvetici
Year: 2023, Volume: 98, Issue: 1, Pages: 135-194 |
| ISSN: | 1420-8946 |
| DOI: | 10.4171/CMH/551 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.4171/CMH/551 Verlag, lizenzpflichtig, Volltext: https://ems.press/journals/cmh/articles/10799725 
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| Author Notes: | James Farre |
| Summary: | For a given pseudo-Anosov homeomorphism q) of a closed surface S, the action of q) on the Teichmuller space T (S) preserves the Weil-Petersson symplectic form. We give explicit formulae for two invariant functions T (S) R whose symplectic gradients generate autonomous Hamiltonian flows that coincide with the action of q) at time one. We compute the Poisson bracket between these two functions. This amounts to computing the variation of length of a Holder cocycle on one lamination along a shear vector field defined by another. For a measurably generic set of laminations, we prove that the variation of length is expressed as the cosine of the angle between the two laminations integrated against the product Holder distribution, generalizing a result of Kerckhoff. We also obtain rates of convergence for the supports of germs of differentiable paths of measured laminations in the Hausdorff metric on a hyperbolic surface, which may be of independent interest. |
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| Item Description: | Gesehen am 27.06.2023 |
| Physical Description: | Online Resource |
| ISSN: | 1420-8946 |
| DOI: | 10.4171/CMH/551 |