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On the length of largest cycle of quadratic dynamical systems modulo a prime
Linnaeus University, Faculty of Technology, Department of Mathematics.
2017 (English)Independent thesis Basic level (degree of Bachelor), 15 credits / 22,5 HE creditsStudent thesis
Abstract [en]

In this paper, we investigate dynamical systems which are given by f : x 7→ x2 + c modulo a prime and for which value of the constant c can we get the largest possible cycle. We get the main ideas for finding cycles in iteration functions by introducing Floyd’s algorithm. Next, we implement the algorithms and ideas for finding cycles in Mathematica and visualize the results. In addition, we study the theoretical bounds for the length of the largest cycle and the case of c = 0 in detail. At last, we have some short discussion to this effect.

Place, publisher, year, edition, pages
2017.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-68047OAI: oai:DiVA.org:lnu-68047DiVA, id: diva2:1143186
Subject / course
Mathematics
Educational program
Applied Mahtematics Programme, 180 credits
Supervisors
Examiners
Available from: 2017-09-22 Created: 2017-09-20 Last updated: 2017-09-22Bibliographically approved

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf