Height bound and preperiodic points for jointly regular families of rational maps

ChongGyu Lee

Published 2010-03-16, updated 2010-04-26Version 2

Silverman proved a height inequality for jointly regular family of rational maps and the author improved it for jointly regular pairs. In this paper, we provide the same improvement for jointly regular family; if S is a jointly regular set of rational maps, then \sum_{f\in S} \dfrac{1}{\deg f} h\bigl(f(P) \bigr) > (1+ \dfrac{1}{r}) f(P) - C where r = \max_{f\in S} r(f).