Department of Mathematics

Prof. Dr. Magnus Aspenberg, Universität Lund: "On semi-hyperbolic maps"

Jul 06, 2017 from 02:00 PM to 03:30 PM

LMS 4 - Raum 526 - Übungsraum

Abstract:

I will discuss the measure theoretic picture for the so called semi-hyperbolic maps, introduced by Carleson, Jones and Yoccoz in 1994. A semi-hyperbolic rational map is a non-hyperbolic map without parabolic periodic points and such that every critical point on the Julia set is non-recurrent. I will show that these maps have Lebesgue measure zero in the parameter space of rational maps, generalizing earlier similar results on so called Misiurewicz maps, which have the stronger property that the whole critical set, instead of every single critical point, on the Julia set is non-recurrent. I also plan to discuss some open questions in relation to this.

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