Higher bifurcations for polynomial skew products

<p style='text-indent:20px;'>We continue our investigation of the parameter space families polynomial skew products. Assuming that base has a Julia set not totally disconnected and is neither Chebyshev nor power map, we prove that, near any bifurcation parameter, one can find parameters where <inline-formula><tex-math id="M1">\begin{document}$ k $\end{document}</tex-math></inline-formula> critical points bifurcate <i>independently</i>, with id="M2">\begin{document}$ up to dimension space. This striking difference respect one-dimensional case. The proof based on variant inclination lemma, applied postcritical at Misiurewicz parameter. By means an analytical criterion for non-vanishing self-intersections current, deduce equality supports current measure such families. Combined results by Dujardin Taflin, this also implies support in these non-empty interior. As part construct, families, subfamilies codimension 1 locus non empty provides new independent existence holomorphic arbitrarily large whose Finally, it shows Hausdorff maximal point its support.</p>