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arXiv · 1111.5554

Explosion of smoothness for conjugacies between multimodal maps

Jose F. Alves·Vilton Pinheiro·Alberto A. Pinto
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Abstract

Let $f$ and $g$ be smooth multimodal maps with no periodic attractors and no neutral points. If a topological conjugacy $h$ between $f$ and $g$ is $C^{1}$ at a point in the nearby expanding set of $f$, then $h$ is a smooth diffeomorphism in the basin of attraction of a renormalization interval of $f$. In particular, if $f:I \to I$ and $g:J \to J$ are $C^r$ unimodal maps and $h$ is $C^{1}$ at a boundary of $I$ then $h$ is $C^r$ in $I$.

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Jose F. Alves, Vilton Pinheiro, Alberto A. Pinto. 2011-11-23. Explosion of smoothness for conjugacies between multimodal maps. https://doi.org/10.1112/jlms%2Fjdt055

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