Minimal sets for flows on moduli space. (English) Zbl 1052.37025
Summary: Let \(S\) be a compact orientable surface, let \(Q\) be the moduli space of quadratic differentials on \(S\) and let \({\mathcal M}\) be a stratum in \(Q\). We explicitly describe the minimal sets for the (Teichmüller) horocycle flow on \({\mathcal M}\) and on \({\mathcal Q}\), and show that these correspond to horizontal cylindrical decompositions of \(S\).
MSC:
| 37D40 | Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) |
| 37F10 | Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets |
| 37B05 | Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) |
| 57M50 | General geometric structures on low-dimensional manifolds |
Keywords:
Teichmüller disks; strata; rational polygonal billiards; interval exchange transformation; quadratic differentials; minimal sets; horocycle flowReferences:
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