Which sequences are orbits?

A. Nicks, Daniel; J. Sixsmith, David

Abstract

In the study of discrete dynamical systems, we typically start with a function from a space into itself, and ask questions about the properties of sequences of iterates of the function. In this paper we reverse the direction of this study. In particular, restricting to the complex plane, we start with a sequence of complex numbers and study the functions (if any) for which this sequence is an orbit under iteration. This gives rise to questions of existence and of uniqueness. We resolve some questions, and show that these issues can be quite delicate.

Citation

A. Nicks, D., & J. Sixsmith, D. (2021). Which sequences are orbits?. Analysis and Mathematical Physics, 11(2), Article 53. https://doi.org/10.1007/s13324-021-00493-5

• Journal Article Type: Article
• Acceptance Date: Jan 29, 2021
• Online Publication Date: Feb 10, 2021
• Publication Date: Feb 10, 2021
• Deposit Date: Feb 12, 2021
• Publicly Available Date: Feb 12, 2021
• Journal: Analysis and Mathematical Physics
• Print ISSN: 1664-2368
• Electronic ISSN: 1664-235X
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 11
• Issue: 2
• Article Number: 53
• DOI: https://doi.org/10.1007/s13324-021-00493-5
• Keywords: Mathematical Physics; Algebra and Number Theory; Analysis
• Public URL: https://nottingham-repository.worktribe.com/output/2463262
• Publisher URL: https://link.springer.com/article/10.1007/s13324-021-00493-5
• Additional Information: Nicks, D.A., Sixsmith, D.J. Which sequences are orbits?. Anal.Math.Phys. 11, 53 (2021). https://doi.org/10.1007/s13324-021-00493-5