Accumulation of periodic points for local uniformly quasiregular mappings
classification
🧮 math.DS
math.CV
keywords
pointsperiodicaccumulationlocalquasiregularuniformlyclosedjulia
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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.
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