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Tr. Mat. Inst. Steklova, 2005, Volume 249, Pages 3–239 (Mi tm28)  

This article is cited in 8 scientific papers (total in 9 papers)

Nonlocal asymptotic behavior of curves and leaves of laminations on universal coverings

D. V. Anosova, E. V. Zhuzhomab

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

Abstract: This monograph is devoted to the properties of infinite (either in one direction or in both directions) curves without self-intersections on closed surfaces. The properties considered are those that are exhibited when the curves are lifted to the universal covering and are associated with the asymptotic behavior of the lifted curves at infinity; these properties mainly manifest themselves when the curves are compared with geodesics or with curves of constant geodesic curvature. The approach described can be applied to the trajectories of flows (which leads to a far-reaching generalization of the Poincaré rotation numbers) and to the leaves of foliations and laminations.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2005, 249, 1–221

Bibliographic databases:
UDC: 517.9+513.8

Citation: D. V. Anosov, E. V. Zhuzhoma, “Nonlocal asymptotic behavior of curves and leaves of laminations on universal coverings”, Tr. Mat. Inst. Steklova, 249, Nauka, MAIK Nauka/Inteperiodika, M., 2005, 3–239; Proc. Steklov Inst. Math., 249 (2005), 1–221

Citation in format AMSBIB
\by D.~V.~Anosov, E.~V.~Zhuzhoma
\paper Nonlocal asymptotic behavior of curves and leaves of laminations on universal coverings
\serial Tr. Mat. Inst. Steklova
\yr 2005
\vol 249
\pages 3--239
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\jour Proc. Steklov Inst. Math.
\yr 2005
\vol 249
\pages 1--221

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    This publication is cited in the following articles:
    1. D. V. Anosov, “On the Projects “Inverse Monodromy Problems and Isomonodromic Deformations,” “Wave Processes in Media with Diffusion,” and “Nonlinear Dynamics of Low-Dimensional Systems with Irregular Behavior of Trajectories””, Proc. Steklov Inst. Math., 251 (2005), 3–5  mathnet  mathscinet  zmath
    2. S. Kh. Aranson, I. A. Gorelikova, E. V. Zhuzhoma, “Closed cross-sections of irrational flows on surfaces”, Sb. Math., 197:2 (2006), 173–192  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. Panov D., “Foliations with Unbounded Deviation on T–2”, Journal of Modern Dynamics, 3:4 (2009), 589–594  crossref  mathscinet  zmath  isi  scopus
    4. Koropecki A., Tal F.A., “Area-Preserving Irrotational Diffeomorphisms of the Torus With Sublinear Diffusion”, Proc. Amer. Math. Soc., 142:10 (2014), 3483–3490  crossref  mathscinet  zmath  isi  scopus
    5. S. M. Aseev, V. M. Buchstaber, R. I. Grigorchuk, V. Z. Grines, B. M. Gurevich, A. A. Davydov, A. Yu. Zhirov, E. V. Zhuzhoma, M. I. Zelikin, A. B. Katok, A. V. Klimenko, V. V. Kozlov, V. P. Leksin, M. I. Monastyrskii, A. I. Neishtadt, S. P. Novikov, E. A. Sataev, Ya. G. Sinai, A. M. Stepin, “Dmitrii Viktorovich Anosov (obituary)”, Russian Math. Surveys, 70:2 (2015), 369–381  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    6. Bel'mesova S.S., Efremova L.S., “On the Concept of Integrability for Discrete Dynamical Systems. Investigation of Wandering Points of Some Trace Map.”, Nonlinear Maps and their Applications, Springer Proceedings in Mathematics & Statistics, Springer Proceedings in Mathematics & Statistics, eds. LopezRuiz R., FournierPrunaret D., Nishio Y., Gracio C., Springer, 2015, 127–158  crossref  mathscinet  zmath  isi  scopus
    7. 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  crossref  mathscinet  zmath  isi  scopus
    8. Nikolaev I.V., “On a Problem of a. Weil”, Beitr. Algebr. Geom., 59:4 (2018), 689–696  crossref  mathscinet  zmath  isi  scopus
    9. V. Z. Grines, E. D. Kurenkov, “Diffeomorphisms of 2-manifolds with one-dimensional spaciously situated basic sets”, Izv. Math., 84:5 (2020), 862–909  mathnet  crossref  crossref  isi
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