Almost sure continuity along curves traversing the Mandelbrot set
SPEAKER | Michael Benedicks
DATE | May 9(Tue), 2017
TIME | 16:05
PLACE | 1503
ABSTRACT | We study continuity properties of dynamical quantities while crossing the Mandelbrot set through typical smooth curves. In particular, we prove that for almost every parameter c0c0 in the boundary of the Mandelbrot set MM with respect of the harmonic measure and every smooth curve ャ:[?1,1]??ャ:[?1,1]?C with the property that c0=ャ(0)c0=ャ(0) there exists a set ?ャAャ having 00 as a Lebesgue density point and such that that limx≧0HDim(Jャ(x))=HDim(Jc0)limx≧0HDim(Jャ(x))=HDim(Jc0) for the Julia sets JcJc. This is joint work with Jacek Graczyk.