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On the space of ergodic measures for the horocycle flow on strata of abelian differentials
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Chaika, Jon, Khalil, Osama and Smillie, John (2023) On the space of ergodic measures for the horocycle flow on strata of abelian differentials. Annales Scientifiques de l'Ecole Normale Superieure . ISSN 0012-9593. (In Press)
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Abstract
We study the horocycle flow on the stratum of abelian differentials H(2). We show that there is a sequence of horocycle ergodic measures, each supported on a periodic horocycle orbit, which weakly converges to an invariant, but non-ergodic, measure by SL2(R). As a consequence, we show that there are points in H(2) whose horocycle flow orbits do not equidistribute towards any invariant measure.
Item Type: | Journal Article | ||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
Library of Congress Subject Headings (LCSH): | Equations, Abelian , Ergodic Theory, Moduli theory | ||||||||||||
Journal or Publication Title: | Annales Scientifiques de l'Ecole Normale Superieure | ||||||||||||
Publisher: | Societe Mathematique de France | ||||||||||||
ISSN: | 0012-9593 | ||||||||||||
Official Date: | 2023 | ||||||||||||
Dates: |
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Status: | Peer Reviewed | ||||||||||||
Publication Status: | In Press | ||||||||||||
Reuse Statement (publisher, data, author rights): | Chaika, Jon, Khalil, Osama and Smillie, John (2023) On the space of ergodic measures for the horocycle flow on strata of abelian differentials. Annales Scientifiques de l'Ecole Normale Superieure . ISSN 0012-9593. (In Press) | ||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
Date of first compliant deposit: | 30 October 2023 | ||||||||||||
Date of first compliant Open Access: | 30 October 2023 | ||||||||||||
RIOXX Funder/Project Grant: |
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