GT ADG-Systèmes DynamiquesCollet, Eckmann and the bifurcation measure
Matthieu Astorg (travail en collaboration avec Thomas Gauthier, Nicolae Mihalache et Gabriel Vigny)
Tuesday 10 October 2017 14:00 - Orléans - Salle de Séminaire
In the space of rational maps of degree d, the bifurcation locus is defined as the set of parameters for which the dynamics on the Julia set is not preserved under small perturbation. By work of DeMarco and Bassannelli-Berteloot, one can define a "bifurcation measure" that is a finite measure whose support is strictly contained in the the bifurcation locus. The support of that measure consists in parameters that bifurcate maximally in some sense. We will show that this support has positive Lebesgue measure in parameter space: in other words, maximal bifurcations are abundant.