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
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.
PDF file (3986 kB)
Mathematics of the USSR-Izvestiya, 1989, 32:3, 449–474
MSC: Primary 58F25; Secondary 34C35, 34C40
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
\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.
\jour Math. USSR-Izv.
Citing articles on Google Scholar:
Related articles on Google Scholar:
Cycle of papers
This publication is cited in the following articles:
D. V. Anosov, “On infinite curves on the Klein bottle”, Math. USSR-Sb., 66:1 (1990), 41–58
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
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
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
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
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
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
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
D. V. Anosov, “Flows on Closed Surfaces and Related Geometrical Questions”, Proc. Steklov Inst. Math., 236 (2002), 12–18
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
S. Kh. Aranson, E. V. Zhuzhoma, “On asymptotic directions of semitrajectories of analytic flows on surfaces”, Russian Math. Surveys, 57:6 (2002), 1207–1209
N.G. Markley, M.H. Vanderschoot, “Remote limit points on surfaces”, Journal of Differential Equations, 188:1 (2003), 221
S. Kh. Aranson, E. V. Zhuzhoma, “Nonlocal Properties of Analytic Flows on Closed Orientable Surfaces”, Proc. Steklov Inst. Math., 244 (2004), 2–17
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
S. Kh. Aranson, I. A. Gorelikova, E. V. Zhuzhoma, “Closed cross-sections of irrational flows on surfaces”, Sb. Math., 197:2 (2006), 173–192
|Number of views:|