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Computational aspects of monomial dynamical systems
Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
2010 (English)In: Computer journal, ISSN 0010-4620, E-ISSN 1460-2067, Vol. 53, no 4, 365-369 p.Article in journal (Refereed) Published
Abstract [en]

We consider the dynamics of xxn, where n ≥ 2 is an integer, over the multiplicative group modulo pk, where k is a positive integer and p an odd prime. This paper is a review of earlier results by the author, but new results are also contained. Possible applications to pseudorandom number generation will be discussed. The main results are a description of the preperiodic points and an algorithm to find the longest possible cycle. The preperiodic points form trees, all isomorphic as graphs to the preperiodic points of the fixed point 1. When n is a prime, different from p, we can describe the tree structure completely. A formula for the length of the longest cycle is presented. We can find one of the longest cycles of the monomial system using a primitive root modulo pk as an initial value.

Place, publisher, year, edition, pages
Oxford University Press, 2010. Vol. 53, no 4, 365-369 p.
National Category
Discrete Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-28136DOI: 10.1093/comjnl/bxm100OAI: oai:DiVA.org:lnu-28136DiVA: diva2:640677
Available from: 2013-08-14 Created: 2013-08-14 Last updated: 2017-12-06Bibliographically approved

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Nilsson, Marcus

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