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Measured foliations on nonorientable surfaces. (English) Zbl 0722.57010

The authors prove the following Theorem: If M is a nonorientable closed surface of negative Euler characteristic, then almost all measured foliations on M have a compact leaf which is a one-sided curve. The proof relies on the study of linear involutions, which generalize the interval exchange transformations. The approach covers also the Masur’s theorem concerning the case when M is orientable.
Reviewer: D.Motreanu (Iaşi)

MSC:

57R30 Foliations in differential topology; geometric theory
37C85 Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\)
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References:

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