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math.NT2021
Stochastic Equidistribution and Generalized Adelic Measures
John Doyle, Paul Fili, Bella Tobin
We study the dynamics of stochastic families of rational maps on the projective line. As such families can be infinite and may not typically be defined over a single number field,…
math.NT2021
Wandering points for the Mahler measure
Paul Fili, Lukas Pottmeyer, Mingming Zhang
Mahler's measure defines a dynamical system on the algebraic numbers. In this paper, we study the problem of which number fields have points which wander under the iteration of Mah…
math.NT2021
Dynatomic polynomials, necklace operators, and universal relations for dynamical units
John R. Doyle, Paul Fili, Trevor Hyde
Given a generic polynomial , the generalized dynatomic polynomial vanishes at precisely those such that has period exactly under iteration of…