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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Wandering domains for infinitely renormalizable diffeomorphisms of the disk

Authors: Christian Bonatti, Jean-Marc Gambaudo, Jean-Marie Lion and Charles Tresser
Journal: Proc. Amer. Math. Soc. 122 (1994), 1273-1278
MSC: Primary 58F12; Secondary 34C27, 34C28
MathSciNet review: 1223264
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Abstract | References | Similar Articles | Additional Information

Abstract: Denjoy's theorem and counter-example for circle maps have counterparts for infinitely renormalizable diffeomorphisms of the 2-disk.

References [Enhancements On Off] (What's this?)

  • [B] 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,
  • [BF] Rufus Bowen and John Franks, The periodic points of maps of the disk and the interval, Topology 15 (1976), no. 4, 337–342. MR 0431282 (55 #4283)
  • [D] A. Denjoy, Sur les courbes définies par les équations différentielles à la surface du tore, J. Math. Pures Appl. (9) 11 (1932), 333-375.
  • [GST] J.-M. Gambaudo, S. van Strien, and C. Tresser, The periodic orbit structure of orientation preserving diffeomorphisms on 𝐷² with topological entropy zero, Ann. Inst. H. Poincaré Phys. Théor. 50 (1989), no. 3, 335–356 (English, with French summary). MR 1017968 (90j:57008)
  • [S] 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 (93k:58194)

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Additional Information

PII: S 0002-9939(1994)1223264-0
Article copyright: © Copyright 1994 American Mathematical Society

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