Bulletin of the Brazilian Mathematical Society, New Series ( IF 0.602 ) Pub Date : 2020-08-01 , DOI: 10.1007/s00574-020-00228-3
Lukas Geyer

We prove that unicritical polynomials $$f(z)=z^d+c$$ which are semihyperbolic, i.e., for which the critical point 0 is a non-recurrent point in the Julia set, are uniformly expanding on the Julia set with respect to the metric $$\rho (z) |dz|$$, where $$\rho (z) = 1+{{\,\mathrm{dist}\,}}(z,P(f))^{-1+1/d}$$ has singularities on the postcritical set P(f). We also show that this metric is Hölder equivalent to the usual Euclidean metric.

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