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
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.

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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