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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. Anosova, E. V. Zhuzhomab

a Steklov Mathematical Institute, Russian Academy of Sciences
b Nizhny Novgorod State Technical University
References:
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
\Bibitem{AnoZhu05}
\by D.~V.~Anosov, E.~V.~Zhuzhoma
\paper Nonlocal asymptotic behavior of curves and leaves of laminations on universal coverings
\serial Trudy Mat. Inst. Steklova
\yr 2005
\vol 249
\pages 3--239
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm28}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2200607}
\zmath{https://zbmath.org/?q=an:1126.37002|1121.37001}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2005
\vol 249
\pages 1--221
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  • This publication is cited in the following 15 articles:
    1. 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  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    2. E. V. Zhuzhoma, “Chaotic Laminations and Their Properties”, Math. Notes, 112:1 (2022), 150–153  mathnet  crossref  crossref  mathscinet
    3. E. V. Zhuzhoma, V. S. Medvedev, “Necessary and sufficient conditions for the conjugacy of Smale regular homeomorphisms”, Sb. Math., 212:1 (2021), 57–69  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. V. Z. Grines, E. V. Zhuzhoma, E. D. Kurenkov, “On DA-endomorphisms of the two-dimensional torus”, Sb. Math., 212:5 (2021), 698–725  mathnet  crossref  crossref  zmath  adsnasa  isi  elib
    5. Efremova L.S., “Geometrically Integrable Maps in the Plane and Their Periodic Orbits”, Lobachevskii J. Math., 42:10, SI (2021), 2315–2324  crossref  mathscinet  isi
    6. 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  mathscinet  zmath  adsnasa  isi  elib
    7. Efremova L.S., “Small Perturbations of Smooth Skew Products and Sharkovsky'S Theorem”, J. Differ. Equ. Appl., 26:8 (2020), 1192–1211  crossref  mathscinet  isi
    8. Nikolaev I.V., “On a Problem of a. Weil”, Beitr. Algebr. Geom., 59:4 (2018), 689–696  crossref  mathscinet  zmath  isi  scopus
    9. 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
    10. 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
    11. 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
    12. 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
    13. Panov D., “Foliations with Unbounded Deviation on T–2”, Journal of Modern Dynamics, 3:4 (2009), 589–594  crossref  mathscinet  zmath  isi  scopus
    14. 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
    15. 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
    Citing articles in Google Scholar: Russian citations, English citations
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