The supports of higher bifurcation currents

2012/02/15 by Romain Dujardin, Dujardin, Romain
Mathematics · #37F45 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #math.CV #math.DS #msc:37F45

paper · pdf · doi:10.48550/arxiv.1202.3249

13 pages

arxiv created 2012/02/15 · arxiv updated 2012/02/16

Abstract

Let (f_λ) be a holomorphic family of rational mappings of degree d on the Riemann sphere, with k marked critical points c₁,..., c_k, parameterized by a complex manifold Λ. To this data is associated a closed positive current T₁\wedge ... \wedge T_k of bidegree (k,k) on Λ, aiming to describe the simultaneous bifurcations of the marked critical points. In this note we show that the support of this current is accumulated by parameters at which c₁,..., c_k eventually fall on repelling cycles. Together with results of Buff, Epstein and Gauthier, this leads to a complete characterization of Supp(T₁\wedge ... \wedge T_k).

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