Diophantine approximation and primitive prime divisors in random iterations
Volume 211 / 2023
Acta Arithmetica 211 (2023), 369-387
MSC: Primary 37P05; Secondary 11J68, 37P30.
DOI: 10.4064/aa230303-12-8
Published online: 14 November 2023
Abstract
We show that, under some mild conditions, the orbit of an algebraic number under random iterations cannot approach another algebraic number very fast. As an application of this result, we prove that, in certain cases, all but finitely many terms in such an orbit have a primitive prime divisor, in the sense that it does not divide any prior terms.
