Flowability of plane homeomorphisms

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

Annales de l’institut Fourier (2012)

  • Volume: 62, Issue: 2, page 619-639
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Le Roux, Frédéric, et al. "Flowability of plane homeomorphisms." Annales de l’institut Fourier 62.2 (2012): 619-639. <http://eudml.org/doc/251097>.

@article{LeRoux2012,
abstract = {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.},
affiliation = {Université Paris Sud, Laboratoire de mathématiques, Bat. 425, 91405 Orsay Cedex, France; National Univeristy of Ireland Maynooth, Department of Mathematics, Logic House, Maynooth, County Kildare, Ireland; Chalmers University of Technology, Department of Mathematics, S-412 96 Gőteborg, Sweden; The Open University, Department of Mathematics and Statistics, Milton Keynes, MK7 6AA, United Kingdom},
author = {Le Roux, Frédéric, O’Farrell, Anthony G., Roginskaya, Maria, Short, Ian},
journal = {Annales de l’institut Fourier},
keywords = {Brouwer homeomorphism; flow; foliation; homeomorphism; plane; Reeb component},
language = {eng},
number = {2},
pages = {619-639},
publisher = {Association des Annales de l’institut Fourier},
title = {Flowability of plane homeomorphisms},
url = {http://eudml.org/doc/251097},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Le Roux, Frédéric
AU - O’Farrell, Anthony G.
AU - Roginskaya, Maria
AU - Short, Ian
TI - Flowability of plane homeomorphisms
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 2
SP - 619
EP - 639
AB - 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.
LA - eng
KW - Brouwer homeomorphism; flow; foliation; homeomorphism; plane; Reeb component
UR - http://eudml.org/doc/251097
ER -

References

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  1. S.A. Andrea, On homeomorphisms of the plane, and their embedding in flows, Bull. Amer. Math. Soc. 71 (1965), 381-383 Zbl0125.40001MR172258
  2. F. Béguin, F. Le Roux, Ensemble oscillant d’un homéomorphisme de Brouwer, homéomorphismes de Reeb, Bull. Soc. Math. France 131 (2003), 149-210 Zbl1026.37033MR1988946
  3. C. Godbillon, Fibrés en droites et feuilletages du plan, Enseignement Math. (2) 18 (1972), 213-224 Zbl0252.57007MR336755
  4. A. Haefliger, G. Reeb, Variétés (non séparées) à une dimension et structures feuilletés du plan, Enseignement Math. (2) 3 (1957), 107-125 Zbl0079.17101MR89412
  5. G.D. Jones, The embedding of homeomorphisms of the plane in continuous flows., Pacific J. Math. 41 (1972), 421-436 Zbl0218.54036MR305382
  6. G.D. Jones, On the problem of embedding discrete flows in continuous flows, Dynamical systems II, Proc. int. Symp., Gainesville/Fla. (1982), 565-568 Zbl0549.58030
  7. R.L. Kruse, J.J. Deely, Joint continuity of monotonic functions, Amer. Math. Monthly 76 (1969), 74-76 Zbl0172.33304MR1535243
  8. F. Le Roux, Classes de conjugaison des flots du plan topologiquement équivalents au flot de Reeb, C. R. Acad. Sci. Paris Sér. I Math. 328 (1999), 45-50 Zbl0922.58069MR1674425
  9. W.R. Utz, The embedding of homeomorphisms in continuous flows, Topology Proc. 6 (1981), 159-177 Zbl0491.54035MR650486

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