| Abstract: |
| Understanding the dynamics of flows on infinite-area translation surfaces is complicated by the fact that the flow need not be conservative and thus may not return to a transverse geodesic segment, and so we may not be able to apply standard tools from the theory of interval exchanges to study the dynamics of these surfaces. Motivated by observations made in a project with Rob Niemeyer, though, we can describe an ergodic-theoretic construction that generalizes a special case of such infinite area translation surfaces where self-similarity can be exploited to study dynamics using infinite interval exchanges. In this talk I will describe this construction and mention some preliminary dynamical results. |
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