Flowability of plane homeomorphisms
Annales de l'Institut Fourier, Volume 62 (2012) no. 2, pp. 619-639.

We describe necessary and sufficient conditions for a fixed point free planar homeomorphism that preserves the standard Reeb foliation to embed in a planar flow that leaves the foliation invariant.

Nous considérons les homéomorphismes h du plan, sans point fixe, et préservant le feuilletage de Reeb. Nous décrivons des conditions nécessaires et suffisantes pour que h soit le temps un d’un flot dont les trajectoires sont les feuilles du feuilletage de Reeb.

DOI: 10.5802/aif.2689
Classification: 37E30, 37E35
Keywords: Brouwer homeomorphism, flow, foliation, homeomorphism, plane, Reeb component.
Mot clés : Homéomorphisme de Brouwer, flot, feuilletage, homéomorphisme, plan, composante de Reeb.

Le Roux, Frédéric 1; O’Farrell, Anthony G. 2; Roginskaya, Maria 3; Short, Ian 4

1 Université Paris Sud, Laboratoire de mathématiques, Bat. 425, 91405 Orsay Cedex, France
2 National Univeristy of Ireland Maynooth, Department of Mathematics, Logic House, Maynooth, County Kildare, Ireland
3 Chalmers University of Technology, Department of Mathematics, S-412 96 Gőteborg, Sweden
4 The Open University, Department of Mathematics and Statistics, Milton Keynes, MK7 6AA, United Kingdom
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Le Roux, Frédéric; O’Farrell, Anthony G.; Roginskaya, Maria; Short, Ian. Flowability of plane homeomorphisms. Annales de l'Institut Fourier, Volume 62 (2012) no. 2, pp. 619-639. doi : 10.5802/aif.2689. https://aif.centre-mersenne.org/articles/10.5802/aif.2689/

[1] Andrea, S.A. On homeomorphisms of the plane, and their embedding in flows, Bull. Amer. Math. Soc., Volume 71 (1965), pp. 381-383 | DOI | MR | Zbl

[2] Béguin, F.; Le Roux, F. Ensemble oscillant d’un homéomorphisme de Brouwer, homéomorphismes de Reeb, Bull. Soc. Math. France, Volume 131 (2003) no. 2, pp. 149-210 | Numdam | MR

[3] Godbillon, C. Fibrés en droites et feuilletages du plan, Enseignement Math. (2), Volume 18 (1972), pp. 213-224 | MR | Zbl

[4] Haefliger, A.; Reeb, G. Variétés (non séparées) à une dimension et structures feuilletés du plan, Enseignement Math. (2), Volume 3 (1957), pp. 107-125 | MR | Zbl

[5] Jones, G.D. The embedding of homeomorphisms of the plane in continuous flows., Pacific J. Math., Volume 41 (1972), pp. 421-436 | MR | Zbl

[6] Jones, G.D. On the problem of embedding discrete flows in continuous flows, Dynamical systems II, Proc. int. Symp., Gainesville/Fla. 1981 (1982), pp. 565-568 | Zbl

[7] Kruse, R.L.; Deely, J.J. Joint continuity of monotonic functions, Amer. Math. Monthly, Volume 76 (1969) no. 1, pp. 74-76 | DOI | MR | Zbl

[8] Le Roux, F. Classes de conjugaison des flots du plan topologiquement équivalents au flot de Reeb, C. R. Acad. Sci. Paris Sér. I Math., Volume 328 (1999) no. 1, pp. 45-50 | DOI | MR | Zbl

[9] Utz, W.R. The embedding of homeomorphisms in continuous flows, Topology Proc., Volume 6 (1981) no. 1, pp. 159-177 (1982) | MR | Zbl

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