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We study conditions involving the critical set of a regular polynomial endomorphism f∶ℂ2↦ℂ2 under which all complete external rays from infinity for f have well defined endpoints.

J. reine angew. Math. 611 (2007), 145—161 DOI 10.1515/CRELLE.2007.077 Journal für die reine und angewandte Mathematik ( Walter de Gruyter Berlin New York 2007 Transfinite diameter and the resultant By Laura DeMarco at Chicago, and Robert Rumely at Athens Abstract. We prove a formula for the Fekete-Leja transfinite diameter of the pull- back of a set E HCN by a regular polynomial map F , expressing it in terms of the resultant of the leading part of F and the transfinite diameter of E. We also establish the nonarchi- medean analogue of this formula. A key step