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 Tr. Mat. Inst. Steklova, 1999, Volume 224, Pages 28–55 (Mi tm690)

On the Lifts to the Plane of Semileaves of Foliations on the Torus with a Finite Number of Singularities

D. V. Anosov

Abstract: An example of a semi-infinite non-self-intersecting curve on the torus is constructed having the property such that its lifts to the universal covering plane are at infinite Frechet distance from any lift of any semileaf of any foliation on the torus with a finite number of singular points. Thus for the lifts of the semileaves of such foliations there are fewer possible “types of behavior up to a finite Frechet distance” than for the lifts of arbitrary non-self-intersecting curves.

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English version:
Proceedings of the Steklov Institute of Mathematics, 1999, 224, 20–45

Bibliographic databases:

Document Type: Article
UDC: 517.91/517.93

Citation: D. V. Anosov, “On the Lifts to the Plane of Semileaves of Foliations on the Torus with a Finite Number of Singularities”, Algebra. Topology. Differential equations and their applications, Collection of papers dedicated to the 90th anniversary of academician Lev Semenovich Pontryagin, Tr. Mat. Inst. Steklova, 224, Nauka, MAIK «Nauka/Inteperiodika», M., 1999, 28–55; Proc. Steklov Inst. Math., 224 (1999), 20–45

Citation in format AMSBIB
\Bibitem{Ano99} \by D.~V.~Anosov \paper On the Lifts to the Plane of Semileaves of Foliations on the Torus with a~Finite Number of Singularities \inbook Algebra. Topology. Differential equations and their applications \bookinfo Collection of papers dedicated to the 90th anniversary of academician Lev Semenovich Pontryagin \serial Tr. Mat. Inst. Steklova \yr 1999 \vol 224 \pages 28--55 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm690} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1721353} \zmath{https://zbmath.org/?q=an:0972.57018} \transl \jour Proc. Steklov Inst. Math. \yr 1999 \vol 224 \pages 20--45 

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This publication is cited in the following articles:
1. D. V. Anosov, “Flows on Closed Surfaces and Related Geometrical Questions”, Proc. Steklov Inst. Math., 236 (2002), 12–18
2. D. V. Anosov, E. V. Zhuzhoma, “Asymptotic Behavior of Covering Curves on the Universal Coverings of Surfaces”, Proc. Steklov Inst. Math., 238 (2002), 1–46
3. 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
4. Grines V., Zhuzhoma E., “Around Anosov-Weil Theory”, Modern Theory of Dynamical Systems: a Tribute to Dmitry Victorovich Anosov, Contemporary Mathematics, 692, eds. Katok A., Pesin Y., Hertz F., Amer Mathematical Soc, 2017, 123–154
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