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Towards a bifurcation theory for perturbed monomial dynamical systems modulo a prime
Linnaeus University, Faculty of Technology, Department of Mathematics.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We investigate perturbed monomial dynamical system over Fp given by iterations of x↦xn+c mod p, where c ∈ Fp. Instead of study the systems one at a time we study all of them at the same time. The complex distibution of periodic points is visualized in the so called Periodic Point Diagram, which can be seen as a discrete version of the classical Bifurcation Diagram. We also prove some general results about the distribution of periodic points. We end the article with a conjecture about the total number of periodic points.

National Category
Discrete Mathematics
Research subject
Mathematics, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-28143OAI: oai:DiVA.org:lnu-28143DiVA, id: diva2:640686
Available from: 2013-08-14 Created: 2013-08-14 Last updated: 2016-02-01Bibliographically approved

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arXiv 1304.4491

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Nilsson, Marcus

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CiteExportLink to record
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  • apa
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