On the Number of Periodic Points of Quadratic Dynamical Systems Modulo a Prime
Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
We investigate the number of periodic points of certain discrete quadratic maps modulo prime numbers. We do so by first exploring previously known results for two particular quadratic maps, after which we explain why the methods used in these two cases are hard to adapt to a more general case.
We then perform experiments and find striking patterns in the behaviour of these general cases which suggest that, apart from the two special cases, the number of periodic points of all quadratic maps of this type behave the same. Finally we formulate a conjecture to this effect.
Place, publisher, year, edition, pages
2015. , 24 p.
Discrete dynamical systems, Quadratic maps, Periodic points
IdentifiersURN: urn:nbn:se:lnu:diva-45635OAI: oai:DiVA.org:lnu-45635DiVA: diva2:848337
Subject / course
Nilsson, Marcus, Senior Lecturer
Svensson, Per Anders, Senior Lecturer