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Preperiodic points for families of polynomials (1102.2769v1)
Published 14 Feb 2011 in math.DS, math.AG, and math.NT
Abstract: 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 $f_{\lambda}$.