Lattès maps and the interior of the bifurcation locus

Sébastien Biebler (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We show the existence of open sets of bifurcations near Lattès maps of sufficiently high degree. In particular, every Lattès 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 Lattès map of sufficiently high degree can be perturbed to exhibit this geometry.

Domaines: Systèmes dynamiques [math.DS]

Sébastien Biebler. Lattès maps and the interior of the bifurcation locus. 2018. ⟨hal-01686965v2⟩