In this paper, we study multiplicative dependence of values of polynomials or rational functions over a number field. As an application, we obtain new results on multiplicative dependence in the orbits of a univariate polynomial dynamical system. We also obtain a generalization of the Northcott theorem replacing the finiteness of preperiodic points from a given number field by the finiteness of algebraic integers having two multiplicatively dependent elements in their orbits.
"On Multiplicative Dependence of Values of Rational Functions and a Generalization of the Northcott Theorem." Michigan Math. J. 68 (2) 385 - 407, June 2019. https://doi.org/10.1307/mmj/1556589745