The bungee set in quasiregular dynamics

Nicks, Daniel A.; Sixsmith, David J.

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. https://doi.org/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
• Keywords: Dynamical Systems; Complex Variables
• Public URL: https://nottingham-repository.worktribe.com/output/1212726
• Publisher URL: https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/blms.12215