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Accumulation of periodic points for local uniformly quasiregular mappings

We consider accumulation of periodic points in local uniformly quasiregular dynamics. Given a local uniformly quasiregular mapping $f$ 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.

preprint2013arXivOpen access
Yûsuke OkuyamaPekka Pankka
math.CVmath.DS
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Yûsuke OkuyamaPekka Pankka

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