Infinite type flat surface models of ergodic systems

Kathryn  Lindsey; Rodrigo  Treviño

doi:10.3934/dcds.2016043

Article Contents

2016, Volume 36, Issue 10: 5509-5553. Doi: 10.3934/dcds.2016043

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Infinite type flat surface models of ergodic systems

Kathryn Lindsey^1, and
Rodrigo Treviño^2,

1.
Department of Mathematics, University of Chicago, Chicago, Illinois 60637
2.
Courant Institute of Mathematical Sciences, New York University, New York, New York 10012

Received: March 2015

Revised: March 2016

Published: May 2017

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Abstract

We propose a general framework for constructing and describing infinite type flat surfaces of finite area. Using this method, we characterize the range of dynamical behaviors possible for the vertical translation flows on such flat surfaces. We prove a sufficient condition for ergodicity of this flow and apply the condition to several examples. We present specific examples of infinite type flat surfaces on which the translation flow exhibits dynamical phenomena not realizable by translation flows on finite type flat surfaces.

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Mathematics Subject Classification: Primary: 37E35; Secondary: 37E20, 37A05.

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