Journal of Modern Dynamics (JMD)

The gap distribution of directions in some Schottky groups

Pages: 477 - 499, Volume 11, 2017      doi:10.3934/jmd.2017019

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Xin Zhang - Department of Mathematics, University of Illinois, 1409 W Green Street, Urbana, IL 61801, United States (email)

Abstract: We prove the existence and some properties of the limiting gap distribution for the directions of some Schottky group orbits in the Poincaré disk. A key feature is that the fundamental domains for these groups have infinite area.

Keywords:  Fuchsian groups of the second kind, Patterson-Sullivan measure, gap distribution.
Mathematics Subject Classification:  Primary: 11J71; Secondary: 11N45, 37F35, 22E40.

Received: April 2016;      Revised: May 2017;      Available Online: September 2017.