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Mat. Sb., 1997, Volume 188, Number 7, Pages 3–22 (Mi msb239)  

This article is cited in 4 scientific papers (total in 4 papers)

On continuity of geodesic frameworks of flows on surfaces

S. Kh. Aranson, E. V. Zhuzhoma, V. S. Medvedev


Abstract: For flows on an orientable closed surface $M_g$ of larger genus (that is, of genus $g\geqslant 2$) a special geodesic distribution (the geodesic framework of the flow) is constructed that consists of geodesics with the same asymptotic directions as the trajectories of the flow and that is a complete topological invariant of the irrational flows on such surfaces. The problem of the dependence of the geodesic framework on a perturbation of the flow (or on the parameter of a family of flows) is considered. It is shown that an irreducible elementary irrational geodesic framework of a flow depends continuously on the perturbation of the flow (which is analogous to the continuous dependence of an irrational Poincare rotation number on a perturbation of a flow).

DOI: https://doi.org/10.4213/sm239

Full text: PDF file (347 kB)
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English version:
Sbornik: Mathematics, 1997, 188:7, 955–972

Bibliographic databases:

UDC: 517.917+513.9
MSC: Primary 58F25; Secondary 58F10, 34C35, 34C28, 34D30, 54H20, 53A05
Received: 27.10.1996

Citation: S. Kh. Aranson, E. V. Zhuzhoma, V. S. Medvedev, “On continuity of geodesic frameworks of flows on surfaces”, Mat. Sb., 188:7 (1997), 3–22; Sb. Math., 188:7 (1997), 955–972

Citation in format AMSBIB
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\by S.~Kh.~Aranson, E.~V.~Zhuzhoma, V.~S.~Medvedev
\paper On continuity of geodesic frameworks of flows on surfaces
\jour Mat. Sb.
\yr 1997
\vol 188
\issue 7
\pages 3--22
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\crossref{https://doi.org/10.4213/sm239}
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\transl
\jour Sb. Math.
\yr 1997
\vol 188
\issue 7
\pages 955--972
\crossref{https://doi.org/10.1070/sm1997v188n07ABEH000239}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0031286459}


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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. E. V. Zhuzhoma, “Continuous Dependence of Geodesic Frames in the Hausdorff Metric”, Math. Notes, 77:6 (2005), 862–864  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. D. V. Anosov, E. V. Zhuzhoma, “Nonlocal asymptotic behavior of curves and leaves of laminations on universal coverings”, Proc. Steklov Inst. Math., 249 (2005), 1–221  mathnet  mathscinet  zmath
    3. Budnyts'ka N.V. Rybalkina T.V., “Realization of a Closed 1-Form on Closed Oriented Surfaces”, Ukr. Math. J., 64:6 (2012), 844–856  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    4. Maksymenko S. Polulyakh E., “Foliations With All Non-Closed Leaves on Non-Compact Surfaces”, Methods Funct. Anal. Topol., 22:3 (2016), 266–282  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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