Preperiodic points for families of polynomials

Dragos Ghioca, Liang-Chung Hsia, Thomas Tucker

Published 2011-02-14Version 1

Let $a(\lambda)$ and $b(\lambda)$ be two polynomials with coefficients in complex numbers and let $f_{\lamb$ be a one-parameter family of polynomials indexed by all complex numbers $\lambda$. We study whether there exist infinitely many complex numbers $\lambda$ such that both $a(\lambda)$ and $b(\lambda)$ are preperiodic for $f_{\lambda}$.