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Horocycle dynamics : new invariants and eigenform loci in the stratum H(1,1)
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Bainbridge, Matt, Smillie, John and Weiss, Barak (2020) Horocycle dynamics : new invariants and eigenform loci in the stratum H(1,1). Memoirs of the American Mathematical Society . (In Press)
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WRAP-Horocycle-dynamics-new-invariants-eigenform-loci-stratum-H(1,1)-Smillie-2020.pdf - Accepted Version - Requires a PDF viewer. Download (1308Kb) | Preview |
Abstract
We study dynamics of the horocycle flow on strata of translation surfaces, introduce new invariants for ergodic measures, and analyze the interaction of the horocycle flow and real Rel surgeries. We use this analysis to complete and ex- tend results of Calta and Wortman classifying horocycle-invariant measures in the eigenform loci. In addition we classify the horocycle orbit-closures and prove that every orbit is equidistributed in its orbit-closure. We also prove equidistribution results describing limits of sequences of measures. Our results have applications to the problem of counting closed trajectories on translation surfaces of genus 2.
| Item Type: | Journal Article | |||||||||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||||||||
| Divisions: | Faculty of Science > Mathematics | |||||||||||||||
| Library of Congress Subject Headings (LCSH): | Surfaces , Geometry, Hyperbolic, Hecke algebra, Invariant measures | |||||||||||||||
| Journal or Publication Title: | Memoirs of the American Mathematical Society | |||||||||||||||
| Publisher: | American Mathematical Society | |||||||||||||||
| ISSN: | 0065-9266 | |||||||||||||||
| Official Date: | 2020 | |||||||||||||||
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| Date of first compliant deposit: | 1 July 2020 | |||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||
| Publication Status: | In Press | |||||||||||||||
| Publisher Statement: | First published in Proceedings of the American Mathematical Society in [volume/issue number and year], published by the American Mathematical Society | |||||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||
| RIOXX Funder/Project Grant: |
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