We show that Misiurewicz maps for which the Julia set is not the whole sphere are Lebesgue density points of hyperbolic maps.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm206-0-3, author = {Magnus Aspenberg}, title = {Rational Misiurewicz maps for which the Julia set is not the whole sphere}, journal = {Fundamenta Mathematicae}, volume = {205}, year = {2009}, pages = {41-48}, zbl = {1187.37064}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm206-0-3} }
Magnus Aspenberg. Rational Misiurewicz maps for which the Julia set is not the whole sphere. Fundamenta Mathematicae, Tome 205 (2009) pp. 41-48. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm206-0-3/