Abstract
The flow in a fixed direction on a translation surface S determines a decomposition of S into closed invariant sets, each of which is either periodic or minimal. We study this decomposition for translation surfaces in the hyperelliptic connected components H hyp(2g − 2) and H hyp(g − 1, g − 1) of the corresponding strata of the moduli space of translation surfaces. Specifically, we characterize the pairs of nonnegative integers (p,m) for which there exists a translation surface in H hyp(2g−2) or H hyp(g−1, g−1) with precisely p periodic components and m minimal components. This extends results by Naveh ([Nav08]), who obtained tight upper bounds on numbers of invariant components for each stratum.
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Lindsey, K.A. Counting invariant components of hyperelliptic translation surfaces. Isr. J. Math. 210, 125–146 (2015). https://doi.org/10.1007/s11856-015-1248-7
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DOI: https://doi.org/10.1007/s11856-015-1248-7