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Romain Dujardin
Non-density of stability for holomorphic mappings on $\protect \mathbb{P}^k$
(Non-densité de la stabilité pour les applications holomorphes sur $\protect \mathbb{P}^k$)
Journal de l'École polytechnique — Mathématiques, 4 (2017), p. 813-843, doi: 10.5802/jep.57
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Class. Math.: 37F45, 37F10, 37F15
Mots clés: Dynamique holomorphe en dimension supérieure, J-stabilité, bifurcations, mélangeurs

Résumé - Abstract

Un théorème célèbre dû à Mañé-Sad-Sullivan et Lyubich affirme que les paramètres $J$-stables forment un ouvert dense de toute famille holomorphe de systèmes dynamiques rationnels en dimension $1$. Dans cet article nous montrons que ce résultat ne subsiste pas en dimension supérieure. Plus précisément nous construisons des ouverts contenus dans le lieu de bifurcation des applications holomorphes de degré $d$ de $\mathbb{P}^k(\mathbb{C})$ pour tout $d\ge 2$ et $k\ge 2$.

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