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Izv. Akad. Nauk SSSR Ser. Mat., 1982, Volume 46, Issue 5, Pages 1047–1061 (Mi izv1658)  

This article is cited in 8 scientific papers (total in 8 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.

Full text: PDF file (1720 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1983, 21:2, 341–354

Bibliographic databases:

UDC: 513.83
MSC: 57R30
Received: 15.03.1982

Citation: V. V. Solodov, “Homeomorphisms of the line and a foliation”, Izv. Akad. Nauk SSSR Ser. Mat., 46:5 (1982), 1047–1061; Math. USSR-Izv., 21:2 (1983), 341–354

Citation in format AMSBIB
\Bibitem{Sol82}
\by V.~V.~Solodov
\paper Homeomorphisms of the line and a~foliation
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1982
\vol 46
\issue 5
\pages 1047--1061
\mathnet{http://mi.mathnet.ru/izv1658}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=675530}
\zmath{https://zbmath.org/?q=an:0548.57013|0521.57022}
\transl
\jour Math. USSR-Izv.
\yr 1983
\vol 21
\issue 2
\pages 341--354
\crossref{https://doi.org/10.1070/IM1983v021n02ABEH001794}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. V. Solodov, “Homeomorphisms of the circle and a foliation”, Math. USSR-Izv., 24:3 (1985), 553–566  mathnet  crossref  mathscinet  zmath
    2. V. V. Solodov, “Topological topics in dynamical systems theory”, Russian Math. Surveys, 46:4 (1991), 107–134  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. L. A. Beklaryan, “On the classification of groups of orientation-preserving homeomorphisms of $\mathbb R$. I. Invariant measures”, Sb. Math., 187:3 (1996), 335–364  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. L. A. Beklaryan, “On the classification of groups of orientation-preserving homeomorphisms of $\mathbb R$. II. Projectively-invariant measures”, Sb. Math., 187:4 (1996), 469–494  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. V. K. Mamaev, “Codimension one foliations of flat 3-manifolds”, Sb. Math., 187:6 (1996), 823–833  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. L. A. Beklaryan, “On Analogs of the Tits Alternative for Groups of Homeomorphisms of the Circle and of the Line”, Math. Notes, 71:3 (2002), 305–315  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. L. A. Beklaryan, “Groups of homeomorphisms of the line and the circle. Topological characteristics and metric invariants”, Russian Math. Surveys, 59:4 (2004), 599–660  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. L. A. Beklaryan, “Groups of line and circle homeomorphisms. Metric invariants and questions of classification”, Russian Math. Surveys, 70:2 (2015), 203–248  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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