an:02195981
Zbl 1087.37038
Aranson, S. Kh.; Zhuzhoma, E. V.
Nonlocal properties of analytic flows on closed orientable surfaces
EN
Dynamical systems and related problems of geometry. Collected papers dedicated to the memory of Academician Andrei Andreevich Bolibrukh. Transl. from the Russian. Moscow: Maik Nauka/Interperiodika. Proceedings of the Steklov Institute of Mathematics 244, 2-17 (2004); translation from Tr. Mat. Inst. Steklova 244, 6-22 (2004).
2004
a
37E35 37D40 37C10
analytic flow; orientable surface; nonlocal properties; bounded deviation property
Nonlocal properties of analytic flows on orientable closed hyperbolic surfaces are investigated. It is proved that the analytic vector fields are dense in the space of all \(C^{r}\)-vector fields endowed with the \(C^{r}\)-topology for any integer~\(r\geq 0\). Moreover, results on the points reachable by semitrajectories of analytic flows are proved. The authors also prove that the semitrajectories of an analytic flow have bounded deviation from the geodesics with the same asymptotic direction.
For the entire collection see [Zbl 1064.37002].
Peter Raith (Wien)