SIEGEL-VEECH TRANSFORMS ARE IN L2

被引：9

作者：

Athreya, Jayadev S. ^{[1
]}

Cheung, Yitwah ^{[2
]}

Masur, Howard ^{[3
]}

Ruhr, Rene ^{[4
]}

机构：

[1] Univ Washington, Dept Math, Padelford Hall, Seattle, WA 98195 USA

[2] San Francisco State Univ, Dept Math, Thornton Hall 937,1600 Holloway Ave, San Francisco, CA 94132 USA

[3] Univ Chicago, Dept Math, 5734 South Univ Ave, Chicago, IL 60615 USA

[4] Technion, Fac Math, IL-32000 Haifa, Israel

来源：

JOURNAL OF MODERN DYNAMICS | 2019年 / 14卷

关键词：

Siegel-Veech transform; Abelian differentials; HAUSDORFF DIMENSION; FLOWS; SPACE;

D O I：

10.3934/jmd.2019001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let H denote a connected component of a stratum of translation surfaces. We show that the Siegel-Veech transform of a bounded compactly supported function on R-2 is in L-2(H, mu), where mu is the Lebesgue measure on H, and give applications to bounding error terms for counting problems for saddle connections. We also propose a new invariant associated to SL(2, R)-invariant measures on strata satisfying certain integrability conditions.

引用

页码：1 / 19

页数：19

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