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arXiv · 1703.05365

Bounded height in families of dynamical systems

Laura DeMarco·Dragos Ghioca·Holly Krieger·Khoa D. Nguyen·Thomas J. Tucker·Hexi Ye
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Abstract

Let a and b be algebraic numbers 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 parametrized by t. We prove that the set of all algebraic numbers t for which there exist positive integers m and n such that f_t^m(a)=f_t^n(b) has bounded Weil height. This is a special case of a more general result supporting a new bounded height conjecture in dynamics. Our results fit into the general setting of the principle of unlikely intersections in arithmetic dynamics.

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BibTeXRIS

Laura DeMarco, Dragos Ghioca, Holly Krieger, Khoa D. Nguyen, Thomas J. Tucker, Hexi Ye. 2017-03-15. Bounded height in families of dynamical systems. https://arxiv.org/abs/1703.05365

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