On the structure of homeomorphisms of the open annulus

Lucien Guillou[1]

  • [1] Université Grenoble 1, Institut Fourier B.P. 74, Saint-Martin-d’Hères 38402 France.

Annales de la faculté des sciences de Toulouse Mathématiques (2011)

  • Volume: 20, Issue: 2, page 367-378
  • ISSN: 0240-2963

Abstract

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Let h be a without fixed point lift to the plane of a homeomorphism of the open annulus isotopic to the identity and without wandering point. We show that h admits a h -invariant dense open set O on which it is conjugate to a translation and we study the action of h on the compactly connected components of the closed and without interior set R 2 O .

How to cite

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Guillou, Lucien. "On the structure of homeomorphisms of the open annulus." Annales de la faculté des sciences de Toulouse Mathématiques 20.2 (2011): 367-378. <http://eudml.org/doc/219776>.

@article{Guillou2011,
abstract = {Let $h$ be a without fixed point lift to the plane of a homeomorphism of the open annulus isotopic to the identity and without wandering point. We show that $h$ admits a $h$-invariant dense open set $O$ on which it is conjugate to a translation and we study the action of $h$ on the compactly connected components of the closed and without interior set $\{\bf R\}^2 \setminus O$.},
affiliation = {Université Grenoble 1, Institut Fourier B.P. 74, Saint-Martin-d’Hères 38402 France.},
author = {Guillou, Lucien},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {annulus; homeomorphism; topological dynamics},
language = {eng},
month = {4},
number = {2},
pages = {367-378},
publisher = {Université Paul Sabatier, Toulouse},
title = {On the structure of homeomorphisms of the open annulus},
url = {http://eudml.org/doc/219776},
volume = {20},
year = {2011},
}

TY - JOUR
AU - Guillou, Lucien
TI - On the structure of homeomorphisms of the open annulus
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2011/4//
PB - Université Paul Sabatier, Toulouse
VL - 20
IS - 2
SP - 367
EP - 378
AB - Let $h$ be a without fixed point lift to the plane of a homeomorphism of the open annulus isotopic to the identity and without wandering point. We show that $h$ admits a $h$-invariant dense open set $O$ on which it is conjugate to a translation and we study the action of $h$ on the compactly connected components of the closed and without interior set ${\bf R}^2 \setminus O$.
LA - eng
KW - annulus; homeomorphism; topological dynamics
UR - http://eudml.org/doc/219776
ER -

References

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  2. Béguin (F.), Crovisier (S.) and LEROUX (F.).— Pseudo-rotations of the open annulus, Bull. Braz. Math. Soc. 37, p. 275-306 (2006). Zbl1105.37029MR2266384
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  5. Guillou (L.).— Free lines for homeomorphisms of the open annulus, Trans. AMS, 360, p. 2191-2204 (2008). Zbl1135.37016MR2366979
  6. Homma (T.), Terasaka (H.).— On the structure of the plane translation of Brouwer, Osaka Math. J. 5, p. 233-266 (1953). Zbl0051.14701MR58963
  7. Le Calvez (P.).— Rotation numbers in the infinite annulus, Proc. Amer. Math. Soc. 129, p. 3221-3230 (2001). Zbl0990.37029MR1844997
  8. Leroux (F.).— Bounded recurrent sets for planar homeomorphisms, Ergodic theory Dynam. Systems 19, p. 1085-1091 (1999). Zbl1031.37038MR1709432
  9. Leroux (F.).— Structure des homéomorphismes de Brouwer, Geometry and Topology 9, p. 1689-1774, (2005). Zbl1087.37035MR2175156
  10. Moore (R.L.).— Foundations of Point Set Theory, AMS Colloquium Publications volume XIII (1962). Zbl0192.28901MR150722
  11. Winkelnkemper (H.).— A generalisation of the Poincaré-Birkhoff theorem, Proc. AMS, 102, p. 1028-1030 (1988). Zbl0656.54032MR934887

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