Flat surface models of ergodic systems
arXiv:1406.4807 · doi:10.3934/dcds.2016043
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.
arXiv comment52 pages
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