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Sbornik: Mathematics, 1997, Volume 188, Issue 7, Pages 955–972
DOI: https://doi.org/10.1070/sm1997v188n07ABEH000239
(Mi sm239)
 

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
References:
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).
Received: 27.10.1996
Russian version:
Matematicheskii Sbornik, 1997, Volume 188, Number 7, Pages 3–22
DOI: https://doi.org/10.4213/sm239
Bibliographic databases:
UDC: 517.917+513.9
MSC: Primary 58F25; Secondary 58F10, 34C35, 34C28, 34D30, 54H20, 53A05
Language: English
Original paper language: Russian
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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\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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\jour Sb. Math.
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\vol 188
\issue 7
\pages 955--972
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник - 1992–2005 Sbornik: Mathematics
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    Abstract page:386
    Russian version PDF:194
    English version PDF:22
    References:57
    First page:1
     
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