Abstract
Abstract
Cheng and Newhouse (Ergod. Th. & Dynam. Sys.25 (2005), 1091–1113) proved a variational principle for topological preimage entropy
$h_{\mathrm {pre}}(f)$
:
$$ \begin{align*} h_{\mathrm{pre}}(f)=\sup_{\mu\in\mathcal{M}(X,f)}h_{\mathrm{pre},\mu}(f). \end{align*} $$
Unfortunately, we show in this note that this variational principle is not true.
Funder
National Natural Science Foundation of China
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics