caa a22 4500 47574067X CHVBK 20180406123458.0 cr unu---uuuuu 170329e20001101xx s 000 0 eng 10.1023/A:1026696213559 doi (NATIONALLICENCE)springer-10.1023/A:1026696213559 Properties of the Absolute That Affect Smoothness of Flows on Closed Surfaces [Elektronische Daten] [S. Aranson, E. Zhuzhoma] Let $$M_g^2$$ be a closed orientable surface of genus $$g \geqslant 2$$ , endowed with the structure of a Riemann manifold of constant negative curvature. For the universal covering $$\Delta$$ , there is the notion of absolute, each of whose points determines an asymptotic direction of a bundle of parallel equidirected geodesics. In the paper it is proved that there is a set $$U_g$$ on the absolute having the cardinality of the continuum and such that if an arbitrary flow on $$M_g^2$$ has a semitrajectory whose covering has asymptotic direction defined by a point from $$U_g$$ , then this flow is not analytical and has infinitely many stationary points. Plenum Publishing Corporation, 2000 flow nationallicence closed orientable surface nationallicence foliation nationallicence geodesic nationallicence universal covering nationallicence Lobachevskii plane nationallicence absolute nationallicence asymptotic direction nationallicence Aranson S. Nizhnii Novgorod State Technical University, Russia aut Zhuzhoma E. Nizhnii Novgorod State Technical University, Russia aut Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/5-6(2000-11-01), 695-703 0001-4346 68:5-6<695 2000 68 11006 https://doi.org/10.1023/A:1026696213559 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1026696213559 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Aranson S. Nizhnii Novgorod State Technical University, Russia aut NATIONALLICENCE 700 1- Zhuzhoma E. Nizhnii Novgorod State Technical University, Russia aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/5-6(2000-11-01), 695-703 0001-4346 68:5-6<695 2000 68 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer