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arXiv · 1801.06339

Latt{\`e}s maps and the interior of the bifurcation locus

Sébastien Biebler
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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.

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Sébastien Biebler. 2018-01-19. Latt{\`e}s maps and the interior of the bifurcation locus. https://arxiv.org/abs/1801.06339

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