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

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2005, Volume 249, Pages 3–239 (Mi tm28)

This article is cited in 13 scientific papers (total in 15 papers)

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

D. V. Anosov^a, E. V. Zhuzhoma^b

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

Full-text PDF (1944 kB) Citations (15)

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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.

Bibliographic databases:

Document Type: Book

UDC: 517.9+513.8

Language: Russian

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

Citation in format AMSBIB

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

\serial Trudy Mat. Inst. Steklova

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\vol 249

\pages 3--239

\publ Nauka, MAIK «Nauka/Inteperiodika»

\publaddr M.

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\jour Proc. Steklov Inst. Math.

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\pages 1--221

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https://www.mathnet.ru/eng/tm/v249/p3

This publication is cited in the following 15 articles:

V. L. Arlazarov, A. Ya. Belov, V. O. Bugaenko, V. A. Vassiliev, A. L. Gorodentsev, S. A. Dorichenko, Yu. S. Ilyashenko, V. M. Imaykin, S. I. Komarov, A. G. Kushnirenko, Yu. P. Lysov, A. L. Semenov, V. M. Tikhomirov, A. K. Tolpygo, A. G. Khovanskii, P. A. Yakushkin, I. V. Yaschenko, “Nikolai Nikolaevich Konstantinov (obituary)”, Russian Math. Surveys, 77:3 (2022), 531–541
E. V. Zhuzhoma, “Chaotic Laminations and Their Properties”, Math. Notes, 112:1 (2022), 150–153
E. V. Zhuzhoma, V. S. Medvedev, “Necessary and sufficient conditions for the conjugacy of Smale regular homeomorphisms”, Sb. Math., 212:1 (2021), 57–69
V. Z. Grines, E. V. Zhuzhoma, E. D. Kurenkov, “On $DA$-endomorphisms of the two-dimensional torus”, Sb. Math., 212:5 (2021), 698–725
Efremova L.S., “Geometrically Integrable Maps in the Plane and Their Periodic Orbits”, Lobachevskii J. Math., 42:10, SI (2021), 2315–2324
V. Z. Grines, E. D. Kurenkov, “Diffeomorphisms of 2-manifolds with one-dimensional spaciously situated basic sets”, Izv. Math., 84:5 (2020), 862–909
Efremova L.S., “Small Perturbations of Smooth Skew Products and Sharkovsky'S Theorem”, J. Differ. Equ. Appl., 26:8 (2020), 1192–1211
Nikolaev I.V., “On a Problem of a. Weil”, Beitr. Algebr. Geom., 59:4 (2018), 689–696
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
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
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
Koropecki A., Tal F.A., “Area-Preserving Irrotational Diffeomorphisms of the Torus With Sublinear Diffusion”, Proc. Amer. Math. Soc., 142:10 (2014), 3483–3490
Panov D., “Foliations with Unbounded Deviation on T–2”, Journal of Modern Dynamics, 3:4 (2009), 589–594
S. Kh. Aranson, I. A. Gorelikova, E. V. Zhuzhoma, “Closed cross-sections of irrational flows on surfaces”, Sb. Math., 197:2 (2006), 173–192
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

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Труды Математического института имени В. А. Стеклова

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