Preperiodic points for families of polynomials

Dragos Ghioca; Liang-Chung Hsia; Thomas Tucker

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arXiv · 1102.2769

Preperiodic points for families of polynomials

Dragos Ghioca·Liang-Chung Hsia·Thomas Tucker

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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 $f_{\lambda}$.

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Dragos Ghioca, Liang-Chung Hsia, Thomas Tucker. 2011-02-14. Preperiodic points for families of polynomials. https://arxiv.org/abs/1102.2769

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