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Continuity of the Green function in meromorphic families of polynomials. (English) Zbl 1401.37104
Summary: We prove that along any marked point the Green function of a meromorphic family of polynomials parametrized by the punctured unit disk is the sum of a logarithmic term and a continuous function.

MSC:
37P30 Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems
37F45 Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations (MSC2010)
37P45 Families and moduli spaces in arithmetic and non-Archimedean dynamical systems
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