#### Vol. 7, No. 3, 2013

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Preperiodic points for families of polynomials

### Dragos Ghioca, Liang-Chung Hsia and Thomas J. Tucker

Vol. 7 (2013), No. 3, 701–732
##### Abstract

Let $a\left(\lambda \right),b\left(\lambda \right)\in ℂ\left[\lambda \right]$, and let ${f}_{\lambda }\left(x\right)\in ℂ\left[x\right]$ be a one-parameter family of polynomials indexed by all $\lambda \in ℂ$. We study whether there exist infinitely many $\lambda \in ℂ$ such that both $a\left(\lambda \right)$ and $b\left(\lambda \right)$ are preperiodic for ${f}_{\lambda }$.

##### Keywords
preperiodic points, heights
Primary: 37P05
Secondary: 37P10
##### Milestones
Revised: 25 March 2012
Accepted: 29 March 2012
Published: 23 August 2013
##### Authors
 Dragos Ghioca Department of Mathematics University of British Columbia Vancouver, BC V6T 1Z2 Canada Liang-Chung Hsia Department of Mathematics National Taiwan Normal University Taipei Taiwan Thomas J. Tucker Department of Mathematics University of Rochester Rochester, NY 14627 United States