English

Sphere branched coverings and the growth rate inequality

Dynamical Systems 2016-12-08 v1

Abstract

We show that the growth inequality rate lim sup1nlog(#Fix(fn))logd\limsup \frac{1}{n} \log (\# Fix (f^n))\geq \log d holds for branched coverings of degree dd of the sphere S2S^2 having a completely invariant simply connected region RR with locally connected boundary, except in some degenerate cases with known couterexamples.

Keywords

Cite

@article{arxiv.1612.02356,
  title  = {Sphere branched coverings and the growth rate inequality},
  author = {J. Iglesias and A. Portela and A. Rovella and J. Xavier},
  journal= {arXiv preprint arXiv:1612.02356},
  year   = {2016}
}