Lattès maps and the interior of the bifurcation locus

2018/01/19 by Sébastien Biebler, Biebler, Sébastien · 1 citation
Engineering · Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1801.06339

openalex publication_date 2018/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Non density of stability for holomorphic mappings on P^k

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