Explosion of smoothness for conjugacies between multimodal maps

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 $I$.

22 pages

References in corpus (1)

• Strong statistical stability of non-uniformly expanding maps