| Abstract: |
| Understanding the dynamics of flows on infinite-area translation surfaces is complicated by the fact that the flow need not be conservative and so may not return to a transverse geodesic segment. For special surfaces exhibiting a particular type of self-similarity, however, we may construct a special collection of geodesic segments which flows in transverse directions must intersect. First-return maps to these collections of segments form an infinite interval exchange which also exhibits a self-similarity that we can exploit to study the dynamics of the system. In this talk I will describe the construction of these self-similar interval exchanges and translation surfaces, and give some preliminary results about their dynamics. |
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