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Topological Transitivity on the Torus

Published online by Cambridge University Press:  20 November 2018

Sol Schwartzman
Sol Schwartzman*
Affiliation:
University of Rhode Island, Kingston, Rhode Island 02881 U.S.A.
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Abstract

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T. Ding has shown that a topologically transitive flow on the torus given by a real analytic vector field is orbitally equivalent to a Kronecker flow on the torus, modified so as to have a finite number of fixed points, provided the original flow had only a finite number of fixed points. In this paper it is shown that the assumption that there are only finitely many fixed points is unnecessary.

Keywords

58F25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 4 , 01 December 1994 , pp. 549 - 551
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Ding, T., Topological Transitivity and Metric Transitivity on T2. Dynamical Systems and Related Topics, (ed. K. Shirawa), World Scientific Press, p. 65 Google Scholar
2. Oxtoby, J. C., Stepanoff Flows on the Torus, Proc. Amer. Math. Soc, 1953, p. 982.Google Scholar
3. Stepanoff, W., Sur une extension du théoreème ergodique, Compositio Math. 3(1936), p. 239.Google Scholar
4. Whyburn, G. T., Analytic Topology, Amer. Math. Soc, Colloquium Publications.Google Scholar