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Strong bifurcation loci of full Hausdorff dimension. (Lieux de bifurcation maximale de dimension de Hausdorff totale.) (English. French summary) Zbl 1326.37036
In the moduli space of degree-$$d$$ rational maps, the bifurcation loci is the support of a positive $$(1,1)$$ positive current $$T$$ called the bifurcation current. This current gives rise to a mesaure $$\mu_{\mathrm{bif}}:=(T)^{2d-2}$$. The main result of this work states that the support of $$\mu_{\mathrm{bif}}$$ has maximal Hausdorff dimension $$2(2d-2)$$. As a consequence, the set of degree-$$d$$ rational maps having $$(2d-2)$$ distinct neutral cycles is dense in a set of full Hausdorff dimension.

##### MSC:
 37F45 Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations (MSC2010) 32U15 General pluripotential theory 28A78 Hausdorff and packing measures
##### Keywords:
bifurcation loci; Hausdorff dimension; Misiurewicz map
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