no. 3
Locally connected exceptional minimal sets of surface homeomorphisms
[Ensembles minimaux exceptionnels localement connexes des homéomorphismes des surfaces]
Biś, Andrzej1 ; Nakayama, Hiromichi ; Walczak, Pawel
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, Tome 54 (2004) no. 3, pp. 711-731.

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.

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.

DOI : 10.5802/aif.2031
Classification : 37E30, 37B45
Keywords: locally connected minimal sets, surface homeomorphisms
Mot clés : ensembles minimaux localement connexes, homéomorphismes des surfaces

Biś, Andrzej 1 ; Nakayama, Hiromichi  ; Walczak, Pawel 

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) 
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Biś, Andrzej; Nakayama, Hiromichi; Walczak, Pawel. Locally connected exceptional minimal sets of surface homeomorphisms. Annales de l'Institut Fourier, Tome 54 (2004) no. 3, pp. 711-731. doi : 10.5802/aif.2031. https://aif.centre-mersenne.org/articles/10.5802/aif.2031/

[1] J.M. Aarts; L.G. Oversteegen The dynamics of the Sierpi\'nski curve, Proc. Amer. Math. Soc., Volume 120 (1994), pp. 965-968 | MR | Zbl

[2] A. Biś; H. Nakayama; P. Walczak Modelling minimal foliated spaces with positive entropy (Preprint)

[3] H. Chu Algebraic topology criteria for minimal sets, Proc. Amer. Math. Soc., Volume 13 (1962), pp. 503-508 | MR | Zbl

[4] R.J. Daverman Decompositions of manifolds, Pure and Applied Mathematics, vol. 124, Academic Press, New York, 1986 | MR | Zbl

[5] A. Fathi; M. Herman Existence de difféomorphismes minimaux, Astérisque, Volume 49 (1977), pp. 37-59 | MR | Zbl

[6] E.E. Floyd A nonhomogeneous minimal set, Bull. Amer. Math. Soc., Volume 55 (1949), pp. 957-960 | MR | Zbl

[7] W.H. Gottschalk; G.A. Hedlund Topological dynamics, vol. 36, Amer. Math. Soc. Colloq. Publ., 1955 | MR | Zbl

[8] M. Handel A pathological area preserving 𝒞 ∞ diffeomorphisms of the plane, Proc. Amer. Math. Soc., Volume 86 (1982), pp. 163-168 | MR | Zbl

[9] H. Kato The nonexistence of expansive homeomorphisms of Peano continua in the plane, Topology Appl., Volume 34 (1990), pp. 161-165 | MR | Zbl

[10] A. Katok; B. Hasselblatt Introduction to the modern theory of dynamical systems, Encyclopedia of Mathematics and its Applications, vol. 54, Cambridge University Press, Cambridge, 1995 | MR | Zbl

[11] S. Kim On low dimensional minimal sets, Pacific Math. J., Volume 43 (1972), pp. 171-174 | MR | Zbl

[12] K. Kuratowski Topology II, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe, Warsaw, 1968 | MR

[13] P.D. McSwiggen Diffeomorphisms of the torus with wandering domains, Proc. Amer. Math. Soc., Volume 117 (1993), pp. 1175-1186 | MR | Zbl

[14] R.L. Moore Concerning upper semi-continuous collections of continua, Trans. Amer. Math. Soc., Volume 27 (1925), pp. 416-428 | JFM | MR

[15] A. Norton An area approach to wandering domains for smooth surface endomorphisms, Ergodic Theory Dynam. Systems, Volume 11 (1991), pp. 181-187 | MR | Zbl

[16] A. Norton; D. Sullivan 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] A.N. Starkov Minimal sets of homogeneous flows, Ergodic Theory Dynam. Systems, Volume 15 (1995), pp. 361-377 | MR | Zbl

[18] G.T. Whyburn Topological characterization of the Sierpi\'nski curve, Fund. Math., Volume 45 (1958), pp. 320-324 | MR | Zbl

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