Chaotic dynamics of a quasiregular sine mapping

2012/08/17 by Alastair N. Fletcher, Daniel A. Nicks, Fletcher, Alastair N. +1
Mathematics · #30C65 (Primary) 30D05 #37F10 (Secondary) #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #math.CV #math.DS #msc:30C65 #msc:30D05 #msc:37F10

paper · pdf · doi:10.48550/arxiv.1208.3585

8 pages

arxiv created 2012/08/17 · arxiv updated 2012/08/20

Abstract

This article studies the iterative behaviour of a quasiregular mapping S:\R^d→\R^d that is an analogue of a sine function. We prove that the periodic points of S form a dense subset of \R^d. We also show that the Julia set of this map is \R^d in the sense that the forward orbit under S of any non-empty open set is the whole space \R^d. The map S was constructed by Bergweiler and Eremenko who proved that the escaping set I(S) is also dense in \R^d.

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