Continuity of the Green function in meromorphic families of polynomials. (English) Zbl 1401.37104

Favre, Charles; Gauthier, Thomas

Algebra Number Theory 12, No. 6, 1471-1487 (2018).

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

Keywords:

polynomial dynamics; Green function; degeneration

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