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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).
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
Linking options:
https://www.mathnet.ru/eng/sm239https://doi.org/10.1070/sm1997v188n07ABEH000239 https://www.mathnet.ru/eng/sm/v188/i7/p3
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Abstract page: | 386 | Russian version PDF: | 194 | English version PDF: | 22 | References: | 57 | First page: | 1 |
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