Phase space universality for multimodal maps |
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Authors: | Daniel Smania |
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Institution: | 1. IMPA—Rio de Janeiro, BRASIL 2. Departamento de Matemática, ICMC-USP-Campus de S?o Carlos, 668, 13560-970, S?o Carlos, SP, BRASIL
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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. |
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Keywords: | renormalization universality multimodal rigidity hybrid class tower |
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