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Journal Articles Annales de la Fac. des Sc. de Toulouse Year : 2013

The supports of higher bifurcation currents.

Abstract

Let (f_\lambda) be a holomorphic family of rational mappings of degree d on the Riemann sphere, with k marked critical points c_1,..., c_k, parameterized by a complex manifold \Lambda. To this data is associated a closed positive current T_1\wedge ... \wedge T_k of bidegree (k,k) on \Lambda, 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 c_1,..., c_k eventually fall on repelling cycles. Together with results of Buff, Epstein and Gauthier, this leads to a complete characterization of Supp(T_1\wedge ... \wedge T_k)
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Dates and versions

hal-01068570 , version 1 (25-09-2014)

Identifiers

  • HAL Id : hal-01068570 , version 1

Cite

Romain Dujardin. The supports of higher bifurcation currents.. Annales de la Fac. des Sc. de Toulouse, 2013, 22 (3), pp.445-464. ⟨hal-01068570⟩
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