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The supports of higher bifurcation currents
Romain Dujardin
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 22 (2013) no. 3, p. 445-464

Let (f λ ) λΛ be a holomorphic family of rational mappings of degree d on 1 (), with k marked critical points c 1 ,...,c k . To this data is associated a closed positive current T 1 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 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 T k ).

Soit (f λ ) λΛ une famille holomorphe d’applications rationnelles de degré d de 1 (), avec k points critiques marqués c 1 ,...,c k . À cette donnée est associée un courant T 1 T k de bidegré (k,k) sur l’espace des paramètres Λ, 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 c 1 ,...,c k 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 T 1 T k .

Received : 2012-03-07
Accepted : 2012-11-25
Published online : 2014-02-14
@article{AFST_2013_6_22_3_445_0,
     author = {Romain Dujardin},
     title = {The supports of higher bifurcation currents},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 22},
     number = {3},
     year = {2013},
     pages = {445-464},
     zbl = {1314.37032},
     mrnumber = {3113022},
     language = {en},
     url = {https://afst.centre-mersenne.org/item/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. afst.centre-mersenne.org/item/AFST_2013_6_22_3_445_0/

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