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.
On examine les ensembles minimaux exceptionnels localement connexes des homéomorphismes des surfaces. Si la surface est différente de tore, ils sont finis ou composés de courbes simples fermés. Dans le tore, ils peuvent aussi prendre la forme similaire à l'ensemble de Sierpiński.
Keywords: locally connected minimal sets, surface homeomorphisms
Mot clés : ensembles minimaux localement connexes, homéomorphismes des surfaces
Biś, Andrzej 1; Nakayama, Hiromichi ; Walczak, Pawel 
@article{AIF_2004__54_3_711_0, author = {Bi\'s, Andrzej and Nakayama, Hiromichi and Walczak, Pawel}, title = {Locally connected exceptional minimal sets of surface homeomorphisms}, journal = {Annales de l'Institut Fourier}, pages = {711--731}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {54}, number = {3}, year = {2004}, doi = {10.5802/aif.2031}, zbl = {1055.37045}, mrnumber = {2097420}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2031/} }
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 SP - 711 EP - 731 VL - 54 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2031/ DO - 10.5802/aif.2031 LA - en ID - AIF_2004__54_3_711_0 ER -
%0 Journal Article %A Biś, Andrzej %A Nakayama, Hiromichi %A Walczak, Pawel %T Locally connected exceptional minimal sets of surface homeomorphisms %J Annales de l'Institut Fourier %D 2004 %P 711-731 %V 54 %N 3 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2031/ %R 10.5802/aif.2031 %G en %F AIF_2004__54_3_711_0
Biś, Andrzej; Nakayama, Hiromichi; Walczak, Pawel. Locally connected exceptional minimal sets of surface homeomorphisms. Annales de l'Institut Fourier, Volume 54 (2004) no. 3, pp. 711-731. doi : 10.5802/aif.2031. https://aif.centre-mersenne.org/articles/10.5802/aif.2031/
[1] The dynamics of the Sierpi\'nski curve, Proc. Amer. Math. Soc., Volume 120 (1994), pp. 965-968 | MR | Zbl
[2] Modelling minimal foliated spaces with positive entropy (Preprint)
[3] Algebraic topology criteria for minimal sets, Proc. Amer. Math. Soc., Volume 13 (1962), pp. 503-508 | MR | Zbl
[4] Decompositions of manifolds, Pure and Applied Mathematics, vol. 124, Academic Press, New York, 1986 | MR | Zbl
[5] Existence de difféomorphismes minimaux, Astérisque, Volume 49 (1977), pp. 37-59 | MR | Zbl
[6] A nonhomogeneous minimal set, Bull. Amer. Math. Soc., Volume 55 (1949), pp. 957-960 | MR | Zbl
[7] Topological dynamics, vol. 36, Amer. Math. Soc. Colloq. Publ., 1955 | MR | Zbl
[8] A pathological area preserving diffeomorphisms of the plane, Proc. Amer. Math. Soc., Volume 86 (1982), pp. 163-168 | MR | Zbl
[9] The nonexistence of expansive homeomorphisms of Peano continua in the plane, Topology Appl., Volume 34 (1990), pp. 161-165 | MR | Zbl
[10] Introduction to the modern theory of dynamical systems, Encyclopedia of Mathematics and its Applications, vol. 54, Cambridge University Press, Cambridge, 1995 | MR | Zbl
[11] On low dimensional minimal sets, Pacific Math. J., Volume 43 (1972), pp. 171-174 | MR | Zbl
[12] Topology II, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe, Warsaw, 1968 | MR
[13] Diffeomorphisms of the torus with wandering domains, Proc. Amer. Math. Soc., Volume 117 (1993), pp. 1175-1186 | MR | Zbl
[14] Concerning upper semi-continuous collections of continua, Trans. Amer. Math. Soc., Volume 27 (1925), pp. 416-428 | JFM | MR
[15] An area approach to wandering domains for smooth surface endomorphisms, Ergodic Theory Dynam. Systems, Volume 11 (1991), pp. 181-187 | MR | Zbl
[16] Wandering domains and invariant conformal structures for mappings of the 2-torus, Ann. Acad. Sci. Fenn. Math., Volume 21 (1996), pp. 51-68 | MR | Zbl
[17] Minimal sets of homogeneous flows, Ergodic Theory Dynam. Systems, Volume 15 (1995), pp. 361-377 | MR | Zbl
[18] Topological characterization of the Sierpi\'nski curve, Fund. Math., Volume 45 (1958), pp. 320-324 | MR | Zbl
Cited by Sources: