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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
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