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 Tr. Mat. Inst. Steklova, 2002, Volume 238, Pages 5–54 (Mi tm342)

Asymptotic Behavior of Covering Curves on the Universal Coverings of Surfaces

D. V. Anosova, E. V. Zhuzhomab

a Steklov Mathematical Institute, Russian Academy of Sciences
b Nizhny Novgorod State Technical University

Abstract: To date, a large number of publications have appeared that are devoted to the study of asymptotic properties of the lifts of curves without self-intersections to the universal covering and the “collation” of these curves (in a certain sense) with lines of constant geodesic curvature that have the same asymptotic direction as the curves under investigation. This paper contains a survey of the results obtained. The ideas of proofs for the main results and the sketches of constructions for important examples on this subject field are presented.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2002, 238, 1–46

Bibliographic databases:

Document Type: Article
UDC: 517.9+513.8

Citation: D. V. Anosov, E. V. Zhuzhoma, “Asymptotic Behavior of Covering Curves on the Universal Coverings of Surfaces”, Monodromy in problems of algebraic geometry and differential equations, Collected papers, Tr. Mat. Inst. Steklova, 238, Nauka, MAIK «Nauka/Inteperiodika», M., 2002, 5–54; Proc. Steklov Inst. Math., 238 (2002), 1–46

Citation in format AMSBIB
\Bibitem{AnoZhu02} \by D.~V.~Anosov, E.~V.~Zhuzhoma \paper Asymptotic Behavior of Covering Curves on the Universal Coverings of Surfaces \inbook Monodromy in problems of algebraic geometry and differential equations \bookinfo Collected papers \serial Tr. Mat. Inst. Steklova \yr 2002 \vol 238 \pages 5--54 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm342} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1969302} \zmath{https://zbmath.org/?q=an:1030.37029} \transl \jour Proc. Steklov Inst. Math. \yr 2002 \vol 238 \pages 1--46 

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This publication is cited in the following articles:
1. S. Kh. Aranson, E. V. Zhuzhoma, “Nonlocal Properties of Analytic Flows on Closed Orientable Surfaces”, Proc. Steklov Inst. Math., 244 (2004), 2–17
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
3. E. V. Zhuzhoma, “Continuous Dependence of Geodesic Frames in the Hausdorff Metric”, Math. Notes, 77:6 (2005), 862–864
4. S. Kh. Aranson, I. A. Gorelikova, E. V. Zhuzhoma, “Closed cross-sections of irrational flows on surfaces”, Sb. Math., 197:2 (2006), 173–192
5. Panov D., “Foliations with Unbounded Deviation on T–2”, Journal of Modern Dynamics, 3:4 (2009), 589–594
6. Grines V. Zhuzhoma E., “Around Anosov-Weil Theory”, Modern Theory of Dynamical Systems: a Tribute to Dmitry Victorovich Anosov, Contemporary Mathematics, 692, ed. Katok A. Pesin Y. Hertz F., Amer Mathematical Soc, 2017, 123–154
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