Arithmetic dynamical systems generated by iterations of polynomials are challenging mathematical objects with intricate algebraic and number theoretic properties, and very complex behaviour. In this talk, I will discuss old and new results on the tail and cycle structure of univariate monomials and Dickson polynomials over finite fields, with an emphasis on when these are permutation polynomials.

In particular, we generalise several results of Shallit and Vasiga regarding the dynamics of certain Dickson polynomials. Moreover, using a deep result of analytic number theory (a bound on Linnik's constant), we show that even the monomial map induces a very large number of cycles for infinitely many primes.


Johann Blanco

Research Area

University of New South Wales


Fri, 21/10/2016 - 2:00pm to 3:00pm


RC-4082, The Red Centre, UNSW