Please use this identifier to cite or link to this item: https://hdl.handle.net/10216/101605
Author(s): Jose F Alves
Vilton Pinheiro
Alberto A Pinto
Title: Explosion of Smoothness for Conjugacies Between Unimodal Maps
Issue Date: 2011
Abstract: Let f and g be C-r unimodal maps, with r >= 3, topologically conjugated by h and without periodic attractors. If h is strongly differentiable at a point p in the expanding set E(f), with h'(p) not equal 0, then, there is an open renormalization interval J such that h is a C-r diffeomorphism in the basin B(J) of J, and h is not strongly differentiable at any point in I \ B(J). The expanding set E(f) contains all points with positive Lyapunov exponent, and if f has a Milnor's interval cycle attractor A then E(f) has full Lebesgue measure.
Description: Let f and g be C r unimodal maps, with r ≥ 3, topologically conjugated by h and without periodic attractors. If h is differentiable at a point p in the expanding set E(f), with h′(p)≠0, then, there is an open renormalization interval J such that h is a C r diffeomorphism in the basin B(J) of J, and h is not differentiable at any point in I ∖ B(J). The expanding set E(f) contains all points with positive Lyapunov exponent, and if f has a Milnor's interval cycle attractor A then E(f) has full Lebesgue measure.
Subject: Matemática
Mathematics
Scientific areas: Ciências exactas e naturais::Matemática
Natural sciences::Mathematics
URI: https://repositorio-aberto.up.pt/handle/10216/101605
Source: Springer Proceedings in Mathematics
Document Type: Artigo em Livro de Atas de Conferência Internacional
Rights: restrictedAccess
Appears in Collections:FCUP - Artigo em Livro de Atas de Conferência Internacional

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