15 citations · 33 across the 13 of their papers we have counts for
16 papers
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,…
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…
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…
On the behavior of Mahler's measure under iteration
Paul Fili, Lukas Pottmeyer, Mingming Zhang
For an algebraic number we denote by the Mahler measure of . As is again an algebraic number (indeed, an algebraic integer), is a self-map on $\over…
A metric of mutual energy and unlikely intersections for dynamical systems
Paul Fili
We introduce a metric of mutual energy for adelic measures associated to the Arakelov-Zhang pairing. Using this metric and potential theoretic techniques involving discrete approxi…
Quantitative height bounds under splitting conditions
Paul Fili, Lukas Pottmeyer
In an earlier work, the first author and Petsche used potential theoretic techniques to establish a lower bound for the height of algebraic numbers that satisfy splitting condition…