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Renormalization Theory For Multimodal Maps
 Eletronic Preprint, IMPA
, 2001
"... We study the dynamics of the renormalization operator for multimodal maps. In particular, we develop a combinatorial theory for certain kind of multimodal maps. We also prove that renormalizations of innitely renormalizable multimodal maps with same bounded combinatorial type are exponentially c ..."
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Cited by 4 (4 self)
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We study the dynamics of the renormalization operator for multimodal maps. In particular, we develop a combinatorial theory for certain kind of multimodal maps. We also prove that renormalizations of innitely renormalizable multimodal maps with same bounded combinatorial type are exponentially close. Our results imply, for instance, the existence and unicity of periodic points for the renormalization operator with arbitrary combinatorial type.
Topological obstructions to smoothness for infinitely renormalizable maps of the disc
 Nonlinearity
"... Abstract. We analyze the signature type of a cascade of periodic orbits associated to period doubling renormalizable maps of the two dimensional disk. The signature is a sequence of rational numbers which describes how periodic orbits turn each other and is invariant by topological conjugacies that ..."
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Cited by 4 (0 self)
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Abstract. We analyze the signature type of a cascade of periodic orbits associated to period doubling renormalizable maps of the two dimensional disk. The signature is a sequence of rational numbers which describes how periodic orbits turn each other and is invariant by topological conjugacies that preserve orientation. 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 showing that there are topological obstructions to realize infinitely renormalizable maps in the area contracting case. 1.
PHASE SPACE UNIVERSALITY FOR MULTIMODAL MAPS
"... Abstract. We study the dynamics of the renormalization operator for multimodal maps. In particular, we develop a combinatorial theory for certain kind of multimodal maps. We also prove that renormalizations of infinitely renormalizable multimodal maps with same bounded combinatorial type are expo ..."
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Cited by 1 (1 self)
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Abstract. We study the dynamics of the renormalization operator for multimodal maps. In particular, we develop a combinatorial theory for certain kind of multimodal maps. We also prove that renormalizations of infinitely renormalizable multimodal maps with same bounded combinatorial type are exponentially close. Our results imply, for instance, the existence and uniqueness of periodic points for the renormalization operator with arbitrary combinatorial type. 1.
1 RENORMALIZATION THEORY FOR MULTIMODAL MAPS
, 2001
"... Abstract. We study the dynamics of the renormalization operator for multimodal maps. In particular, we prove the exponential convergence of this operator for infinitely renormalizable maps with same bounded combinatorial type. 1. ..."
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Abstract. We study the dynamics of the renormalization operator for multimodal maps. In particular, we prove the exponential convergence of this operator for infinitely renormalizable maps with same bounded combinatorial type. 1.