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

 

Infinitely renormalizable diffeomorphisms
of the disk at the boundary of chaos


Authors: Eleonora Catsigeras, Jean-Marc Gambaudo and Fernando Moreira
Journal: Proc. Amer. Math. Soc. 126 (1998), 297-304
MSC (1991): Primary 58F13
MathSciNet review: 1403117
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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.


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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: http://dx.doi.org/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
Article copyright: © Copyright 1998 American Mathematical Society