Accumulation of periodic points for local uniformly quasiregular mappings

Abstract

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.

arXiv comment17 pages

References in corpus (1)

• Rescaling principle for isolated essential singularities of quasiregular mappings

Cited by in corpus (2)

• The dynamics of quasiregular maps of punctured space
• Obstructions for automorphic quasiregular maps and Lattès-type uniformly quasiregular maps