Bounded Height in Families of Dynamical Systems

 dc.creator DeMarco, L dc.creator Ghioca, D dc.creator Krieger, Holly Christine dc.creator Dang Nguyen, K dc.creator Tucker, T dc.creator Ye, H dc.date.accessioned 2017-07-06 dc.date.accessioned 2018-11-24T23:27:34Z dc.date.available 2017-11-01T15:55:43Z dc.date.available 2018-11-24T23:27:34Z dc.date.issued 2017-08-29 dc.identifier https://www.repository.cam.ac.uk/handle/1810/268021 dc.identifier.uri http://repository.aust.edu.ng/xmlui/handle/123456789/4005 dc.description.abstract Let a, b ∈ $\bar{\mathbb{Q}}$ be such that exactly one of a and b is an algebraic integer, and let f$_{t}$(z) := z$^{2}$ + t be a family of polynomials parameterized by t ∈ $\bar{\mathbb{Q}}$. We prove that the set of all t ∈ $\bar{\mathbb{Q}}$ 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. dc.publisher Oxford University Press dc.publisher International Mathematics Research Notices dc.title Bounded Height in Families of Dynamical Systems dc.type Article
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