Abstract
The first results on this subject are again due to H.Poincaré who showed in particular the rôle of the homeomorphisms of the circle in this context. He discovered the phenomenon of the exceptional homeomorphisms which was further clarified later on by A. Denjoy, as well as the properties of conjugation to rotations which recently were continued by V. Arnold and M. Herman. Furthermore the global qualitative description of direction fields on the torus and on the Klein bottle are due to H. Kneser.
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© 1983 Springer-Verlag Berlin Heidelberg
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Godbillon, C. (1983). Direction Fields on the Torus and Homeomorphisms of the Circle. In: Dynamical Systems on Surfaces. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-68626-9_4
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DOI: https://doi.org/10.1007/978-3-642-68626-9_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-11645-5
Online ISBN: 978-3-642-68626-9
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