On the Hausdorff dimension of the set of non-escaping points in the Julia set

Walter Bergweiler, Weiwei Cui, Lingrui Wang

For an entire function $f$ and a non-zero complex number $\lambda$, let $f_{\lambda }(z)=f(\lambda z)$. We give conditions on $f$ which imply that the Hausdorff dimension of the set of non-escaping poin…