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Izv. Akad. Nauk SSSR Ser. Mat., 1988, Volume 52, Issue 3, Pages 451–478 (Mi izv1189)  

This article is cited in 14 scientific papers (total in 15 papers)

On the behavior in the Euclidean or Lobachevsky plane of trajectories that cover trajectories of flows on closed surfaces. II

D. V. Anosov


Abstract: This paper is a continuation of Part I (Izv. Akad. Nauk SSSR Ser. Mat., 1987, v. 51, № 1, p. 16–43; Math. USSR-Izv. 30 (1988), 15–38). Let $L$ be a (semi) infinite nonselfintersecting continuous curve on a closed surface of nonpositive Euler characteristic and consider the behavior at “infinity” of the curve obtained by lifting $\widetilde L$ to the universal cover: either the Lobachevsky or the Euclidean plane. The possible types of this behavior for arbitrary $\widetilde L$ turn out to be the same as those for $L$ which are semitrajectories of $C^\infty$ flows. Questions concerning the approach of to infinity along a definite direction are again considered. An example is constructed in which all points of the absolute are limit points in $\widetilde L$.
Bibliography: 12 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1989, 32:3, 449–474

Bibliographic databases:

Document Type: Article
UDC: 517.91
MSC: Primary 58F25; Secondary 34C35, 34C40
Received: 16.06.1987

Citation: D. V. Anosov, “On the behavior in the Euclidean or Lobachevsky plane of trajectories that cover trajectories of flows on closed surfaces. II”, Izv. Akad. Nauk SSSR Ser. Mat., 52:3 (1988), 451–478; Math. USSR-Izv., 32:3 (1989), 449–474

Citation in format AMSBIB
\Bibitem{Ano88}
\by D.~V.~Anosov
\paper On~the behavior in the Euclidean or Lobachevsky plane of trajectories that cover trajectories of flows on closed surfaces.~II
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1988
\vol 52
\issue 3
\pages 451--478
\mathnet{http://mi.mathnet.ru/izv1189}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=954292}
\zmath{https://zbmath.org/?q=an:0673.58039}
\transl
\jour Math. USSR-Izv.
\yr 1989
\vol 32
\issue 3
\pages 449--474
\crossref{https://doi.org/10.1070/IM1989v032n03ABEH000776}


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    This publication is cited in the following articles:
    1. D. V. Anosov, “On infinite curves on the Klein bottle”, Math. USSR-Sb., 66:1 (1990), 41–58  mathnet  crossref  mathscinet  zmath  isi
    2. S. Kh. Aranson, E. V. Zhuzhoma, “Trajectories covering flows for branched coverings of the sphere and projective plane”, Math. Notes, 53:5 (1993), 463–468  mathnet  crossref  mathscinet  zmath  isi  elib
    3. S. Kh. Aranson, V. Z. Grines, E. V. Zhuzhoma, “On the geometry and topology of flows and foliations on surfaces and the Anosov problem”, Sb. Math., 186:8 (1995), 1107–1146  mathnet  crossref  mathscinet  zmath  isi
    4. D. V. Anosov, “On the behaviour in the Euclidean or Lobachevsky plane of trajectories that cover trajectories of flows on closed surfaces. III”, Izv. Math., 59:2 (1995), 287–320  mathnet  crossref  mathscinet  zmath  isi
    5. V. I. Arnol'd, A. A. Bolibrukh, R. V. Gamkrelidze, V. P. Maslov, E. F. Mishchenko, S. P. Novikov, Yu. S. Osipov, Ya. G. Sinai, A. M. Stepin, L. D. Faddeev, “Dmitrii Viktorovich Anosov (on his 60th birthday)”, Russian Math. Surveys, 52:2 (1997), 437–445  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    6. A. A. Glutsyuk, “Limit sets at infinity for liftings of non-self-intersecting curves on the torus to the plane”, Math. Notes, 64:5 (1998), 579–589  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. D. V. Anosov, “On the Lifts to the Plane of Semileaves of Foliations on the Torus with a Finite Number of Singularities”, Proc. Steklov Inst. Math., 224 (1999), 20–45  mathnet  mathscinet  zmath
    8. S. Kh. Aranson, E. V. Zhuzhoma, “Properties of the Absolute That Affect Smoothness of Flows on Closed Surfaces”, Math. Notes, 68:6 (2000), 695–703  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. D. V. Anosov, “Flows on Closed Surfaces and Related Geometrical Questions”, Proc. Steklov Inst. Math., 236 (2002), 12–18  mathnet  mathscinet  zmath
    10. 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  mathnet  mathscinet  zmath
    11. S. Kh. Aranson, E. V. Zhuzhoma, “On asymptotic directions of semitrajectories of analytic flows on surfaces”, Russian Math. Surveys, 57:6 (2002), 1207–1209  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    12. N.G. Markley, M.H. Vanderschoot, “Remote limit points on surfaces”, Journal of Differential Equations, 188:1 (2003), 221  crossref
    13. S. Kh. Aranson, E. V. Zhuzhoma, “Nonlocal Properties of Analytic Flows on Closed Orientable Surfaces”, Proc. Steklov Inst. Math., 244 (2004), 2–17  mathnet  mathscinet  zmath
    14. 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  mathnet  mathscinet  zmath
    15. 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
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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