Matematiska institutionen

DNA-seminarium: Almost sure continuity along curves traversing the Mandelbrot set

  • Datum:
  • Plats: Ångströmlaboratoriet 64119
  • Föreläsare: Michael Benedicks
  • Kontaktperson: Michael Benedicks
  • Seminarium

The aim of this talk is to discuss the dimension  and the harmonic measure on the Julia set of f_c(z)=z^2+c, where c is close to the boundary of the Mandelbrot set. The idea is to use work of Graczyk-Swiatek and Smirnov, which proves that for a.e. point c_0 on the boundary of the Mandelbrot set with respect to harmonic measure the corresponding function f_{c_0} satisfies the so called Collet-Eckmann condition: there is exponential derivative growth at the critical value c_0. This will allow us to do parameter selection of the type previously done with Carleson to get exponential derivative growth, along subset of  curves originating in c_0. This is joint work with Jacek Graczyk.