Bifurcations, intersections, and heights

2014/12/08 by DeMarco, Laura · 3 citations
#11G05 #37F45 #37P30 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1412.2708

Abstract

In this article, we prove the equivalence of dynamical stability, preperiodicity, and canonical height 0, for algebraic families of rational maps f_t: ℙ¹(ℂ) → ℙ¹(ℂ), parameterized by t in a quasi-projective complex variety. We use this to prove one implication in the if-and-only-if statement of Conjecture 1.10 in [Baker-DeMarco, 2013] on unlikely intersections in the moduli space of rational maps; we present the conjecture here in a more general form.

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