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arXiv · 1208.3585

Chaotic dynamics of a quasiregular sine mapping

Alastair N. Fletcher·Daniel A. Nicks
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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.

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Alastair N. Fletcher, Daniel A. Nicks. 2012-08-17. Chaotic dynamics of a quasiregular sine mapping. https://arxiv.org/abs/1208.3585

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