Abstract
Important classes of foliations can be obtained by suspension over homeomorphisms and endomorphisms of the unit circle. Thus the methods of one-dimensional dynamics play a distinguished role in the theory of foliations. A modern encyclopaedia of the subject is the monograph:
W. de Melo & S. van Strien, One-dimensional dynamics, Ergebnisse der Mathematik und ihrer Grenzgebiete, 25, Springer-Verlag, 1993.
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Bibliographic Notes
Denjoy, A., 1932 Sur les courbes définies par les équations différentielles à la surface du tore, J. Math. Pures et Appl. (ser 9) 11, 333–375.
Tamura, I., 1976 Topology of Foliations, Moscow, Mir Publisher.
Cherry, T., 1938 Analytic quasi-periodic curves of discontinuous type on torus, Proc. London Math. Soc. 44, 175–215.
Anjos, Dos, 1986 Polynomial vector fields on the torus, Bol. Soc. Bras. Mat. 17(2), 1–22.
Martens M., Strien van S., Melo de W. and Mendes P. 1990 On Cherry flows, Ergod. Th. and Dynam. Sys. 10, 531–554.
Yoccoz, J.-C., 1984 Il n’y a pas de contre-exemple de Denjoy analytique, C.R. Acad. Sc. Paris, t.298, Série I, no. 7, 141–144.
Aranson, S. H., Malkin, M. I. and Zhuzhoma, E. V., 1993 Local structure and smoothness preventing quasiminimality for flows on the torus, Differents. Uravneniya, Translation: Differential Equations 29, 789–791.
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© 2001 Springer-Verlag Berlin Heidelberg
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Nikolaev, I. (2001). Homeomorphisms of the Unit Circle. In: Foliations on Surfaces. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04524-4_9
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DOI: https://doi.org/10.1007/978-3-662-04524-4_9
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