Latt\`es maps and the interior of the bifurcation locus
Abstract
We show the existence of open sets of bifurcations near Latt\`es maps of sufficiently high degree. In particular, every Latt\`es map has an iterate which is in the closure of the interior of the bifurcation locus. To show this, we design a method to intersect the limit set of some particular type of IFS with a well-oriented curve. Then, we show that a Latt\`es map of sufficiently high degree can be perturbed to exhibit this geometry.
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