@article{5aa4067a6af34cd5aedee0c054a4d0df,

title = "Bounded Height in Families of Dynamical Systems",

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.",

author = "Laura DeMarco and Dragos Ghioca and Holly Krieger and {Dang Nguyen}, Khoa and Thomas Tucker and Hexi Ye",

note = "Funding Information: L.D. was partially supported by National Science Foundation grants DMS-1517080 and DMS-1600718. D.G. was partially supported by a Discovery grant from the National Sciences and Engineering Research Council of Canada. H.K. was partially supported by National Science Foundation grant DMS-1303770. K.N. was partially supported by a fellowship from the Pacific Institute for the Mathematical Sciences and T.T. was partially supported by National Science Foundation grant DMS-1200749.",

year = "2019",

doi = "10.1093/imrn/rnx174",

language = "English (US)",

volume = "2019",

pages = "2453--2482",

journal = "International Mathematics Research Notices",

issn = "1073-7928",

publisher = "Oxford University Press",

number = "8",

}