On the Number of Periodic Points of Quadratic Dynamical Systems Modulo a Prime

Sammanfattning: 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.