Open Access
2011 Preimages of quadratic dynamical systems
Benjamin Hutz, Trevor Hyde, Benjamin Krause
Involve 4(4): 343-363 (2011). DOI: 10.2140/involve.2011.4.343


For a quadratic polynomial with rational coefficients, we consider the problem of bounding the number of rational points that eventually land at a given constant after iteration, called preimages of the constant. It was shown by Faber, Hutz, Ingram, Jones, Manes, Tucker, and Zieve (2009) that the number of rational preimages is bounded as one varies the polynomial. Explicit bounds on the number of preimages of zero and 1 were addressed in subsequent articles. This article addresses explicit bounds on the number of preimages of any algebraic number for quadratic dynamical systems and provides insight into the geometric surfaces parameterizing such preimages.


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Benjamin Hutz. Trevor Hyde. Benjamin Krause. "Preimages of quadratic dynamical systems." Involve 4 (4) 343 - 363, 2011.


Received: 13 September 2010; Revised: 14 May 2011; Accepted: 15 May 2011; Published: 2011
First available in Project Euclid: 20 December 2017

zbMATH: 1258.37076
MathSciNet: MR2905234
Digital Object Identifier: 10.2140/involve.2011.4.343

Primary: 14G05 , 37P05
Secondary: 37F10

Keywords: arithmetic geometry , Preimage , quadratic dynamical systems , rational points , uniform bound

Rights: Copyright © 2011 Mathematical Sciences Publishers

Vol.4 • No. 4 • 2011
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