Puri, Y and Ward, T orcid.org/0000-0002-8253-5767 (2001) Arithmetic and growth of periodic orbits. Journal of Integer Sequences, 4 (2). 1. Article 01.2.1-18. ISSN 1530-7638
Abstract
Two natural properties of integer sequences are introduced and studied. The first, exact realizability, is the property that the sequence coincides with the number of periodic points under some map. This is shown to impose a strong inner structure on the sequence. The second, realizability in rate, is the property that the sequence asympototically approximates the number of periodic points under some map. In both cases we discuss when a sequence can have that property. For exact realizability, this amounts to examining the range and domain among integer sequences of the paired transformations
Pern = Σd|nd Orbd; Orbd =1/n Σd|nµ(n/d)Perd ORBIT
that move between an arbitrary sequence of non-negative integers Orb counting the orbits of a map and the sequence Per of periodic points for that map. Several examples from the Encyclopedia of Integer Sequences arise in this work, and a table of sequences from the Encyclopedia known or conjectured to be exactly realizable is given.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 06 Sep 2019 08:51 |
Last Modified: | 06 Sep 2019 08:51 |
Status: | Published |
Publisher: | University of Waterloo |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:149677 |