Superattracting fixed points of quasiregular mappings

Abstract

We investigate the rate of convergence of the iterates of an n-dimensional quasiregular mapping within the basin of attraction of a fixed point of high local index. A key tool is a refinement of a result that gives bounds on the distortion of the image of a small spherical shell. This result also has applications to the rate of growth of quasiregular mappings of polynomial type, and to the rate at which the iterates of such maps can escape to infinity.

12 pages

References in corpus (7)

• Fast escaping points of entire functions
• The escaping set of a quasiregular mapping
• Fatou-Julia theory for non-uniformly quasiregular maps
• The fast escaping set for quasiregular mappings
• The Julia set and the fast escaping set of a quasiregular mapping
• Fixed points of composite entire and quasiregular maps
• Quasiregular dynamics on the n-sphere

Cited by in corpus (2)

• The bungee set in quasiregular dynamics
• Quasiconformality and hyperbolic skew