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Modelling the Number of Periodic Points of Quadratic Maps Using Random Maps
Linnaeus University, Faculty of Technology, Department of Mathematics.
2017 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

Since the introduction of Pollard's rho method for integer factorisation in 1975 there has been great interest in understanding the dynamics of quadratic maps over finite fields. One avenue for this, and indeed the heuristic on which Pollard bases the proof of the method's efficacy, is the idea that quadratic maps behave roughly like random maps.

We explore this heuristic from the perspective of comparing the number of periodic points. We find that empirically random maps appear to model the number of periodic points of quadratic maps well, and moreover prove that the number of periodic points of random maps satisfy an interesting asymptotic behaviour that we have observed experimentally for quadratic maps.

Place, publisher, year, edition, pages
2017. , p. 22
Keywords [en]
arithmetic dynamical systems, periodic points, quadratic maps, random maps
National Category
Discrete Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-65548OAI: oai:DiVA.org:lnu-65548DiVA, id: diva2:1111736
Subject / course
Mathematics
Educational program
Mathematics and Modelling, Master Programme, 120 credits
Supervisors
Examiners
Available from: 2017-06-19 Created: 2017-06-19 Last updated: 2018-05-17Bibliographically 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