Mathematical Research Letters

Volume 13, Issue 3, May 2006 pp. 343-357.

Topological invariance of generic non-uniformly expanding multimodal maps

Authors: Stefano Luzzatto (1), and Lanyu Wang (2)
Author institution: Imperial College (1), and Academy of Mathematics and System Sciences (2)

Summary: We introduce a \emph{Topological Slow Recurrence} condition on the orbits of critical points of multimodal maps and show that this condition is equivalent to the simultaneous occurrence of metric \emph{Slow Recurrence} and \emph{Collet-Eckmann} conditions. In particular, if \( f \) is non-uniformly expanding and the critical points are generic with respect to the absolutely continuous invariant measures, then any map \( g \) topologically conjugate to \( f \) is also non-uniformly expanding.

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