Latt{\`e}s maps and the interior of the bifurcation locus
Dynamical Systems
2020-01-13 v3
Abstract
We show the existence of open sets of bifurcations near Latt{\`e}s maps of sufficiently high degree. In particular, every Latt{\`e}s 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{\`e}s map of sufficiently high degree can be perturbed to exhibit this geometry.
Cite
@article{arxiv.1801.06339,
title = {Latt{\`e}s maps and the interior of the bifurcation locus},
author = {Sébastien Biebler},
journal= {arXiv preprint arXiv:1801.06339},
year = {2020}
}