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arXiv · 2211.03571

The growth rate inequality for Thurston maps with non hyperbolic orbifolds

J. Iglesias·A. Portela·A. Rovella·J. Xavier
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Abstract

Let $f: S^2 \to S^2$ be a continuous map of degree $d$, $|d|>1$, and let $N_nf$ denote the number of fixed points of $f^n$. We show that if $f$ is a Thurston map with non hyperbolic orbifold, then either the growth rate inequality $\limsup \frac{1}{n} \log N_nf\geq \log |d|$ holds for $f$ or $f$ has exactly two critical points which are fixed and totally invariant.

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J. Iglesias, A. Portela, A. Rovella, J. Xavier. 2022-11-07. The growth rate inequality for Thurston maps with non hyperbolic orbifolds. https://arxiv.org/abs/2211.03571

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