Flat surface models of ergodic systems
Dynamical Systems
2023-05-26 v2 Geometric Topology
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.
Keywords
Cite
@article{arxiv.1406.4807,
title = {Flat surface models of ergodic systems},
author = {Kathryn Lindsey and Rodrigo Treviño},
journal= {arXiv preprint arXiv:1406.4807},
year = {2023}
}
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52 pages