Chaotic dynamics of a quasiregular sine mapping
Dynamical Systems
2012-08-20 v1 Complex Variables
Abstract
This article studies the iterative behaviour of a quasiregular mapping S:\R^d\to\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.
Keywords
Cite
@article{arxiv.1208.3585,
title = {Chaotic dynamics of a quasiregular sine mapping},
author = {Alastair N. Fletcher and Daniel A. Nicks},
journal= {arXiv preprint arXiv:1208.3585},
year = {2012}
}
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8 pages