Locally connected exceptional minimal sets of surface homeomorphisms

Andrzej Biś[1]; Hiromichi Nakayama; Pawel Walczak

  • [1] Lódź; University, faculty of mathematics, Banacha 22, 90238 Lódź (Pologne), Hiroshima University, Faculty of Integrated Arts and Sciences, 1-7-1 Kagamiyama, Higashi-Hiroshima, 739-8521 (Japon)

Annales de l’institut Fourier (2004)

  • Volume: 54, Issue: 3, page 711-731
  • ISSN: 0373-0956

Abstract

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We deal with locally connected exceptional minimal sets of surface homeomorphisms. If the surface is different from the torus, such a minimal set is either finite or a finite disjoint union of simple closed curves. On the torus, such a set can admit also a structure similar to that of the Sierpiński curve.

How to cite

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Biś, Andrzej, Nakayama, Hiromichi, and Walczak, Pawel. "Locally connected exceptional minimal sets of surface homeomorphisms." Annales de l’institut Fourier 54.3 (2004): 711-731. <http://eudml.org/doc/116124>.

@article{Biś2004,
abstract = {We deal with locally connected exceptional minimal sets of surface homeomorphisms. If the surface is different from the torus, such a minimal set is either finite or a finite disjoint union of simple closed curves. On the torus, such a set can admit also a structure similar to that of the Sierpiński curve.},
affiliation = {Lódź; University, faculty of mathematics, Banacha 22, 90238 Lódź (Pologne), Hiroshima University, Faculty of Integrated Arts and Sciences, 1-7-1 Kagamiyama, Higashi-Hiroshima, 739-8521 (Japon)},
author = {Biś, Andrzej, Nakayama, Hiromichi, Walczak, Pawel},
journal = {Annales de l’institut Fourier},
keywords = {locally connected minimal sets; surface homeomorphisms},
language = {eng},
number = {3},
pages = {711-731},
publisher = {Association des Annales de l'Institut Fourier},
title = {Locally connected exceptional minimal sets of surface homeomorphisms},
url = {http://eudml.org/doc/116124},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Biś, Andrzej
AU - Nakayama, Hiromichi
AU - Walczak, Pawel
TI - Locally connected exceptional minimal sets of surface homeomorphisms
JO - Annales de l’institut Fourier
PY - 2004
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 3
SP - 711
EP - 731
AB - We deal with locally connected exceptional minimal sets of surface homeomorphisms. If the surface is different from the torus, such a minimal set is either finite or a finite disjoint union of simple closed curves. On the torus, such a set can admit also a structure similar to that of the Sierpiński curve.
LA - eng
KW - locally connected minimal sets; surface homeomorphisms
UR - http://eudml.org/doc/116124
ER -

References

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  15. A. Norton, An area approach to wandering domains for smooth surface endomorphisms, Ergodic Theory Dynam. Systems 11 (1991), 181-187 Zbl0703.58028MR1101089
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