Bounded Height in Families of Dynamical Systems

Laura DeMarco, Dragos Ghioca*, Holly Krieger, Khoa Dang Nguyen, Thomas Tucker, Hexi Ye

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Let a, b € ℚbe such that exactly one of a and b is an algebraic integer, and let ft(z) := z2+t be a family of polynomials parameterized by t € ℚ. We prove that the set of all t €' Q for which there exist m,n ≥ 0 such that f m t (a) = f n t (b) has bounded height. This is a special case of a more general result supporting a new bounded height conjecture in arithmetic dynamics.

Original languageEnglish (US)
Pages (from-to)2453-2482
Number of pages30
JournalInternational Mathematics Research Notices
Volume2019
Issue number8
DOIs
StatePublished - 2019

ASJC Scopus subject areas

  • Mathematics(all)

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