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JOURNALS // Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya // Archive

Izv. Akad. Nauk SSSR Ser. Mat., 1982 Volume 46, Issue 5, Pages 1047–1061 (Mi im1658)

This article is cited in 12 papers

Homeomorphisms of the line and a foliation

V. V. Solodov


Abstract: This paper considers foliations of codimension one and class $C^i$, $i\geqslant0$. Under specified restrictions on the fundamental group of a Novikov component the study of such a foliation can be reduced to studying the representation of the fundamental group as homeomorphisms of the line. As a result theorems are obtained about the existence of a compact leaf. Applications are obtained to the real-analytic foliations and Anosov foliations.
Bibliography: 12 titles.

UDC: 513.83

MSC: 57R30

Received: 15.03.1982


 English version:
Mathematics of the USSR-Izvestiya, 1983, 21:2, 341–354

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© Steklov Math. Inst. of RAS, 2024