Wandering domains for infinitely renormalizable diffeomorphisms of the disk
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- by Christian Bonatti, Jean-Marc Gambaudo, Jean-Marie Lion and Charles Tresser PDF
- Proc. Amer. Math. Soc. 122 (1994), 1273-1278 Request permission
Abstract:
Denjoy’s theorem and counter-example for circle maps have counterparts for infinitely renormalizable diffeomorphisms of the 2-disk.References
- P. Bohl, Über die Hinsichtlich der Unabhängigen und Abhängigen Variabeln Periodische Differentialgleichung Erster Ordnung, Acta Math. 40 (1916), no. 1, 321–336 (German). MR 1555141, DOI 10.1007/BF02418549
- Rufus Bowen and John Franks, The periodic points of maps of the disk and the interval, Topology 15 (1976), no. 4, 337–342. MR 431282, DOI 10.1016/0040-9383(76)90026-4 A. Denjoy, Sur les courbes définies par les équations différentielles à la surface du tore, J. Math. Pures Appl. (9) 11 (1932), 333-375.
- J.-M. Gambaudo, S. van Strien, and C. Tresser, The periodic orbit structure of orientation preserving diffeomorphisms on $D^2$ with topological entropy zero, Ann. Inst. H. Poincaré Phys. Théor. 50 (1989), no. 3, 335–356 (English, with French summary). MR 1017968
- 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. MR 1184622
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 122 (1994), 1273-1278
- MSC: Primary 58F12; Secondary 34C27, 34C28
- DOI: https://doi.org/10.1090/S0002-9939-1994-1223264-0
- MathSciNet review: 1223264