Flows of flowable Reeb homeomorphisms

Shigenori Matsumoto[1]

  • [1] Nihon University Department of Mathematics College of Science and Technology 1-8-14 Kanda, Surugadai, Chiyoda-ku Tokyo, 101-8308 (Japan)

Annales de l’institut Fourier (2012)

  • Volume: 62, Issue: 3, page 887-897
  • ISSN: 0373-0956

Abstract

top
We consider a fixed point free homeomorphism h of the closed band B = × [ 0 , 1 ] which leaves each leaf of a Reeb foliation on B invariant. Assuming h is the time one of various topological flows, we compare the restriction of the flows on the boundary.

How to cite

top

Matsumoto, Shigenori. "Flows of flowable Reeb homeomorphisms." Annales de l’institut Fourier 62.3 (2012): 887-897. <http://eudml.org/doc/251073>.

@article{Matsumoto2012,
abstract = {We consider a fixed point free homeomorphism $h$ of the closed band $B=\mathbb\{R\}\times [0,1]$ which leaves each leaf of a Reeb foliation on $B$ invariant. Assuming $h$ is the time one of various topological flows, we compare the restriction of the flows on the boundary.},
affiliation = {Nihon University Department of Mathematics College of Science and Technology 1-8-14 Kanda, Surugadai, Chiyoda-ku Tokyo, 101-8308 (Japan)},
author = {Matsumoto, Shigenori},
journal = {Annales de l’institut Fourier},
keywords = {Reeb foliations; homeomorphisms; topological conjugacy},
language = {eng},
number = {3},
pages = {887-897},
publisher = {Association des Annales de l’institut Fourier},
title = {Flows of flowable Reeb homeomorphisms},
url = {http://eudml.org/doc/251073},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Matsumoto, Shigenori
TI - Flows of flowable Reeb homeomorphisms
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 3
SP - 887
EP - 897
AB - We consider a fixed point free homeomorphism $h$ of the closed band $B=\mathbb{R}\times [0,1]$ which leaves each leaf of a Reeb foliation on $B$ invariant. Assuming $h$ is the time one of various topological flows, we compare the restriction of the flows on the boundary.
LA - eng
KW - Reeb foliations; homeomorphisms; topological conjugacy
UR - http://eudml.org/doc/251073
ER -

References

top
  1. LEJ Brouwer, Beweis des Ebenen Translationssatzes, Math. Ann. 72 (1912), 37-54 Zbl43.0569.02MR1511684
  2. François Béguin, Frédéric Le Roux, Ensemble oscillant d’un homéomorphisme de Brouwer, homéomorphismes de Reeb, Bull. Soc. Math. France 131 (2003), 149-210 Zbl1026.37033MR1988946
  3. Béla De Kerékjártó, Sur le groupe des transformations topologiques du plan, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (2) 3 (1934), 393-400 Zbl0010.03902MR1556737
  4. Albert Fathi, An orbit closing proof of Brouwer’s lemma on translation arcs, Enseign. Math. (2) 33 (1987), 315-322 Zbl0649.54022MR925994
  5. John Franks, A new proof of the Brouwer plane translation theorem, Ergodic Theory Dynam. Systems 12 (1992), 217-226 Zbl0767.58025MR1176619
  6. Lucien Guillou, Théorème de translation plane de Brouwer et généralisations du théorème de Poincaré-Birkhoff, Topology 33 (1994), 331-351 Zbl0924.55001MR1273787
  7. André Haefliger, Georges Reeb, Variétés (non séparées) à une dimension et structures feuilletées du plan, Enseignement Math. (2) 3 (1957), 107-125 Zbl0079.17101MR89412
  8. Tatsuo Homma, Hidetaka Terasaka, On the structure of the plane translation of Brouwer, Osaka Math. J. 5 (1953), 233-266 Zbl0051.14701MR58963
  9. F. Le Roux, A. G. O’Farrell, M. Roginskaya, I. Short, Flowability of plane homeomorphisms 
  10. Frédéric 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
  11. Hiromichi Nakayama, A non-flowable plane homeomorphism whose non-Hausdorff set consists of two disjoint lines, Houston J. Math. 21 (1995), 569-572 Zbl0857.54040MR1352607

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.