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Infinitely renormalizable diffeomorphisms of the disk at the boundary of chaos
Author(s):
Eleonora
Catsigeras;
Jean-Marc
Gambaudo;
Fernando
Moreira
Journal:
Proc. Amer. Math. Soc.
126
(1998),
297-304.
MSC (1991):
Primary 58F13
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Abstract:
We show that, among area contracting embeddings of the 2-disk, infinitely renormalizable maps with a bounded geometry either have positive topological entropy or correspond to a cascade of period doubling.
References:
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- R. Bowen and J. Franks, ``The periodic points of maps of the disk and the interval,'' Topology 15 (1976), 337-342. MR 55:4283
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- E. Catsigeras, ``Cascades of period doubling of stable codimension one,'' IMPA's thesis, 1994.
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- [GT2]
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Additional Information:
Eleonora
Catsigeras
Affiliation:
Facultad de Ingeneria IMERL, C.C. 30, Montevideo, Uruguay
Email:
eleonora@fing.edu.uy
Jean-Marc
Gambaudo
Affiliation:
I.N.L.N., 1361, route des lucioles, Sophia-Antipolis, 06560 Valbonne, France
Email:
gambaudo@inln.cnrs.fr
Fernando
Moreira
Affiliation:
Departamento de Matemática, Faculdade de Ciências do Porto, Praça Gomes Teixeira, 4000 Porto, Portugal
Email:
fsmoreir@fc.up.pt
DOI:
10.1090/S0002-9939-98-03945-8
PII:
S 0002-9939(98)03945-8
Received by editor(s):
June 5, 1996
Communicated by:
Linda Keen
Copyright of article:
Copyright
1998,
American Mathematical Society
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