Let be a holomorphic family of rational mappings of degree on , with marked critical points . To this data is associated a closed positive current of bidegree on , 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 eventually fall on repelling cycles. Together with results of Buff, Epstein and Gauthier, this leads to a complete characterization of .
Soit une famille holomorphe d’applications rationnelles de degré de , avec points critiques marqués . À cette donnée est associée un courant de bidegré sur l’espace des paramètres , visant à décrire les bifurcations simultanées des points critiques marqués. Dans cette note nous montrons que le support de ce courant est accumulé par des paramètres en lesquels tombent sur des cycles répulsifs. En combinant ceci avec des résultats de Buff, Epstein et Gauthier, on obtient ainsi une caractérisation complète du support de .
@article{AFST_2013_6_22_3_445_0, author = {Dujardin, Romain}, title = {The supports of higher bifurcation currents}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {445--464}, publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques}, address = {Toulouse}, volume = {Ser. 6, 22}, number = {3}, year = {2013}, doi = {10.5802/afst.1378}, mrnumber = {3113022}, zbl = {1314.37032}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/afst.1378/} }
TY - JOUR AU - Dujardin, Romain TI - The supports of higher bifurcation currents JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2013 SP - 445 EP - 464 VL - 22 IS - 3 PB - Université Paul Sabatier, Institut de mathématiques PP - Toulouse UR - http://archive.numdam.org/articles/10.5802/afst.1378/ DO - 10.5802/afst.1378 LA - en ID - AFST_2013_6_22_3_445_0 ER -
%0 Journal Article %A Dujardin, Romain %T The supports of higher bifurcation currents %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2013 %P 445-464 %V 22 %N 3 %I Université Paul Sabatier, Institut de mathématiques %C Toulouse %U http://archive.numdam.org/articles/10.5802/afst.1378/ %R 10.5802/afst.1378 %G en %F AFST_2013_6_22_3_445_0
Dujardin, Romain. The supports of higher bifurcation currents. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 22 (2013) no. 3, pp. 445-464. doi : 10.5802/afst.1378. http://archive.numdam.org/articles/10.5802/afst.1378/
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