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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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
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  • 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
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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