F J Moreira 2004 Nonlinearity 17 1547 doi:10.1088/0951-7715/17/5/001
Topological obstructions to smoothness for infinitely renormalizable maps of the disc
F J Moreira
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We analyse the signature type of a cascade of periodic orbits associated with period-doubling renormalizable maps of the two-dimensional disc. The signature is a sequence of rational numbers invariant with respect to orientation-preserving topological conjugacies, which describes how periodic orbits are linked around each other. We prove that in the class of area-contracting maps the signature cannot be a monotone sequence. This explains why classical examples of infinitely renormalizable maps due to Bowen, Franks and Young cannot be achieved by smooth dissipative maps, which shows that there are topological obstructions to realizing infinitely renormalizable maps in the area-contracting case.
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Issue 5 (September 2004)
Received 18 July 2003, in final form 15 April 2004
Published 27 May 2004
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Topological obstructions to smoothness for infinitely renormalizable maps of the disc
F J Moreira 2004 Nonlinearity 17 1547
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