Counting saddle connections in a homology class modulo \begin{document}$ \boldsymbol q $\end{document} (with an appendix by Rodolfo Gutiérrez-Romo)

IF 0.7 1区数学 Q2 MATHEMATICS

Journal of Modern Dynamics Pub Date : 2019-08-23 DOI:10.3934/JMD.2019020

Michael Magee, René Rühr

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引用次数: 1

摘要

我们给出了平移表面上鞍形连接数的有效估计，这些鞍形连接的长度为\begin｛document｝$\leq L$\end｛document｝，并且在一个规定的同调类modulo \ begin{document｝$q$\end{document}中。相对于地层上的Masur–Veech测度，我们的估计适用于平移曲面的模量空间的地层中的几乎所有平移曲面。

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Counting saddle connections in a homology class modulo \begin{document}$ \boldsymbol q $\end{document} (with an appendix by Rodolfo Gutiérrez-Romo)

We give effective estimates for the number of saddle connections on a translation surface that have length \begin{document}$ \leq L $\end{document} and are in a prescribed homology class modulo \begin{document}$ q $\end{document} . Our estimates apply to almost all translation surfaces in a stratum of the moduli space of translation surfaces, with respect to the Masur–Veech measure on the stratum.

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来源期刊

Journal of Modern Dynamics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Modern Dynamics (JMD) is dedicated to publishing research articles in active and promising areas in the theory of dynamical systems with particular emphasis on the mutual interaction between dynamics and other major areas of mathematical research, including: Number theory Symplectic geometry Differential geometry Rigidity Quantum chaos Teichmüller theory Geometric group theory Harmonic analysis on manifolds. The journal is published by the American Institute of Mathematical Sciences (AIMS) with the support of the Anatole Katok Center for Dynamical Systems and Geometry at the Pennsylvania State University.