Effective counting on translation surfaces

Effective counting on translation surfaces

We prove an effective version of a celebrated result of Eskin and Masur: for any SL2(R)-invariant locus L of translation surfaces, there exists κ>0, such that for almost every translation surface in L, the number of saddle connections with holonomy vector of length at most T, grows like cT2+O(T2−...

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Veröffentlicht in:Advances in mathematics (New York. 1965) 2020-01, Vol.360, p.106890, Article 106890
Hauptverfasser: Nevo, Amos, Rühr, Rene, Weiss, Barak
Format: Artikel
Sprache:eng
Schlagworte:
Counting asymptotics
Effective Ergodic Theorem
Saddle connections
Translation surfaces
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Zusammenfassung:We prove an effective version of a celebrated result of Eskin and Masur: for any SL2(R)-invariant locus L of translation surfaces, there exists κ>0, such that for almost every translation surface in L, the number of saddle connections with holonomy vector of length at most T, grows like cT2+O(T2−κ). We also provide effective versions of counting in sectors and in ellipses.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2019.106890