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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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Official URL: https://www.ams.org/cgi-bin/mstrack/accepted_paper...

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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
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
Dates:
DateEvent
2020Available
24 August 2019Accepted
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:
Project/Grant IDRIOXX Funder NameFunder ID
359821Simons Foundationhttp://dx.doi.org/10.13039/100000893
2010428Royal Societyhttp://dx.doi.org/10.13039/501100000288
2010428.United States-Israel Binational Science Foundationhttp://dx.doi.org/10.13039/501100001742
DLGAPS 27989[ERC] Horizon 2020 Framework Programmehttp://dx.doi.org/10.13039/100010661
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