Differentiability and topology of labyrinths in the disc and annulus (Q1089962)

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.