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Wandering domains for infinitely renormalizable diffeomorphisms of the disk. (English) Zbl 0843.57016
Summary: Denjoy’s theorem and counter-example for circle maps have counterparts for infinitely renormalizable diffeomorphisms of the 2-disk.

MSC:
57M99 General low-dimensional topology
37-XX Dynamical systems and ergodic theory
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[3] A. Denjoy, Sur les courbes définies par les équations différentielles à la surface du tore, J. Math. Pures Appl. (9) 11 (1932), 333-375. · JFM 58.1124.04
[4] J.-M. Gambaudo, S. van Strien, and C. Tresser, The periodic orbit structure of orientation preserving diffeomorphisms on \?² with topological entropy zero, Ann. Inst. H. Poincaré Phys. Théor. 50 (1989), no. 3, 335 – 356 (English, with French summary). · Zbl 0701.58030
[5] Dennis Sullivan, Bounds, quadratic differentials, and renormalization conjectures, American Mathematical Society centennial publications, Vol. II (Providence, RI, 1988) Amer. Math. Soc., Providence, RI, 1992, pp. 417 – 466. · Zbl 0936.37016
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