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The bungee set in quasiregular dynamics

Nicks, Daniel A.; Sixsmith, David J.

Authors

David J. Sixsmith



Abstract

In complex dynamics, the bungee set is defined as the set points whose orbit is neither bounded nor tends to infinity. In this paper we study, for the first time, the bungee set of a quasiregular map of transcendental type. We show that this set is infinite, and shares many properties with the bungee set of a transcendental entire function. By way of contrast, we give examples of novel properties of this set in the quasiregular setting. In particular, we give an example of a quasiconformal map of the plane with a non-empty bungee set; this behaviour is impossible for an analytic homeomorphism.

Citation

Nicks, D. A., & Sixsmith, D. J. (2019). The bungee set in quasiregular dynamics. Bulletin of the London Mathematical Society, 51(1), 120-128. doi:10.1112/blms.12215

Journal Article Type Article
Acceptance Date Oct 19, 2018
Online Publication Date Nov 5, 2018
Publication Date 2019-02
Deposit Date Oct 31, 2018
Publicly Available Date Nov 6, 2019
Journal Bulletin of the London Mathematical Society
Print ISSN 0024-6093
Electronic ISSN 1469-2120
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 51
Issue 1
Pages 120-128
DOI https://doi.org/10.1112/blms.12215
Public URL https://nottingham-repository.worktribe.com/output/1212726
Publisher URL https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/blms.12215

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