Preperiodic points for families of polynomials

Ghioca, Dragos; Hsia, Liang-Chung; Tucker, Thomas

doi:10.2140/ant.2013.7.701

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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

DOI: 10.2140/ant.2013.7.701

Abstract

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

Keywords

preperiodic points, heights

Mathematical Subject Classification 2010

Primary: 37P05

Secondary: 37P10

Milestones

Received: 21 September 2011

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

Vol. 7, No. 3, 2013