Accumulation of periodic points for local uniformly quasiregular mappings
Dynamical Systems
2015-05-20 v1 Complex Variables
Abstract
We consider accumulation of periodic points in local uniformly quasiregular dynamics. Given a local uniformly quasiregular mapping with a countable and closed set of isolated essential singularities and their accumulation points on a closed Riemannian manifold, we show that points in the Julia set are accumulated by periodic points. If, in addition, the Fatou set is non-empty and connected, the accumulation is by periodic points in the Julia set itself. We also give sufficient conditions for the density of repelling periodic points.
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Cite
@article{arxiv.1306.3298,
title = {Accumulation of periodic points for local uniformly quasiregular mappings},
author = {Yûsuke Okuyama and Pekka Pankka},
journal= {arXiv preprint arXiv:1306.3298},
year = {2015}
}
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17 pages