Non density of stability for holomorphic mappings on P^k

2016/10/06 by Romain Dujardin, Dujardin, Romain · 5 citations
Mathematics · #Meromorphic and Entire Functions #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1610.01785

Abstract

A well-known theorem due to Ma ~n 'e-Sad-Sullivan and Lyubich asserts that\nJ-stable maps are dense in any holomorphic family of rational maps in dimension\n1. In this paper we show that the corresponding result fails in higher\ndimension. More precisely, we construct open subsets in the bifurcation locus\nin the space of holomorphic mappings of degree d of P^k (C) for every d \≥ 2\nand k \≥ 2.\n

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• Misiurewicz parameters and dynamical stability of polynomial-like maps of large topological degree

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