In the moduli space of degree rational maps, the bifurcation locus is the support of a closed positive current which is called the bifurcation current. This current gives rise to a measure whose support is the seat of strong bifurcations. Our main result says that has maximal Hausdorff dimension . As a consequence, the set of degree rational maps having distinct neutral cycles is dense in a set of full Hausdorff dimension.
Dans l’espace des modules des fractions rationnelles de degré , le lieu de bifurcation est le support d’un -courant positif fermé qui est appelé courant de bifurcation. Ce courant induit une mesure dont le support est le siège de bifurcations maximales. Notre principal résultat stipule que est de dimension de Hausdorff maximale . Par conséquent, l’ensemble des fractions rationnelles de degré possédant cycles neutres distincts est dense dans un ensemble de dimension de Hausdorff totale.
Keywords: complex dynamics, bifurcations, pluripotential theory, Hausdorff dimension
Mot clés : dynamique holomorphe, bifurcations, théorie du pluripotentiel, dimension de Hausdorff
@article{ASENS_2012_4_45_6_947_0, author = {Gauthier, Thomas}, title = {Strong bifurcation loci of full {Hausdorff} dimension}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {947--984}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {Ser. 4, 45}, number = {6}, year = {2012}, doi = {10.24033/asens.2181}, mrnumber = {3075109}, language = {en}, url = {http://archive.numdam.org/articles/10.24033/asens.2181/} }
TY - JOUR AU - Gauthier, Thomas TI - Strong bifurcation loci of full Hausdorff dimension JO - Annales scientifiques de l'École Normale Supérieure PY - 2012 SP - 947 EP - 984 VL - 45 IS - 6 PB - Société mathématique de France UR - http://archive.numdam.org/articles/10.24033/asens.2181/ DO - 10.24033/asens.2181 LA - en ID - ASENS_2012_4_45_6_947_0 ER -
%0 Journal Article %A Gauthier, Thomas %T Strong bifurcation loci of full Hausdorff dimension %J Annales scientifiques de l'École Normale Supérieure %D 2012 %P 947-984 %V 45 %N 6 %I Société mathématique de France %U http://archive.numdam.org/articles/10.24033/asens.2181/ %R 10.24033/asens.2181 %G en %F ASENS_2012_4_45_6_947_0
Gauthier, Thomas. Strong bifurcation loci of full Hausdorff dimension. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 45 (2012) no. 6, pp. 947-984. doi : 10.24033/asens.2181. http://archive.numdam.org/articles/10.24033/asens.2181/
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