Vol. 12, No. 6, 2018
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Continuity of the Green function in meromorphic families of polynomials

Charles Favre and Thomas Gauthier
Vol. 12 (2018), No. 6, 1471–1487
DOI: 10.2140/ant.2018.12.1471
Abstract

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.

Keywords
polynomial dynamics, Green function, degeneration
Mathematical Subject Classification 2010
Primary: 37P30
Secondary: 37F45, 37P45
Milestones
Received: 29 June 2017
Revised: 8 December 2017
Accepted: 5 January 2018
Published: 6 October 2018
Authors
Charles Favre
Centre de Mathématiques Laurent Schwartz, Ecole Polytechnique
CNRS, Université Paris-Saclay
Palaiseau
France
Thomas Gauthier
Laboratoire Amiénois de Mathématiques Fondamentales et Appliquées
Université de Picardie Jules Verne
Amiens
France		 Centre de Mathématiques Laurent Schwartz, Ecole Polytechnique
CNRS, Université Paris-Saclay
Palaiseau
France