Lattès maps and the interior of the bifurcation locus

Abstract : 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.
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Contributor : Sébastien Biebler <>
Submitted on : Tuesday, January 7, 2020 - 12:09:35 PM
Last modification on : Monday, January 13, 2020 - 1:11:41 AM

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  • HAL Id : hal-01686965, version 3
  • ARXIV : 1801.06339

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Sébastien Biebler. Lattès maps and the interior of the bifurcation locus. 2020. ⟨hal-01686965v3⟩

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