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arXiv · 1612.02356

Sphere branched coverings and the growth rate inequality

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

We show that the growth inequality rate $$\limsup \frac{1}{n} \log (\# Fix (f^n))\geq \log d$$ holds for branched coverings of degree $d$ of the sphere $S^2$ having a completely invariant simply connected region $R$ with locally connected boundary, except in some degenerate cases with known couterexamples.

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J. Iglesias, A. Portela, A. Rovella, J. Xavier. 2016-12-07. Sphere branched coverings and the growth rate inequality. https://arxiv.org/abs/1612.02356

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