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Differentiability and topology of labyrinths in the disc and annulus. (English) Zbl 0621.57013

A foliation F of a surface M is called arational if F has no interior compact leaf, F is transverse to \(\delta\) M, and no separatrices join two singularities. Theorem: Let F be an arational foliation of the disc or annulus. If F is of class \(C^ 2\), then every regular leaf is compact. The authors also give a classification of arational foliations of a disc and of an annulus in the case when singularities are thorns and saddles with any number of prongs.
Reviewer: A.Piatkowski

MSC:

57R30 Foliations in differential topology; geometric theory
37C10 Dynamics induced by flows and semiflows
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
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