CAPA: Critical points of the multiplier map

  • Date:
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 74118
  • Lecturer: Igors Gorbovickis
  • Contact person: Alejandro Luque
  • Seminarium

Abstract: The multiplier of a non-parabolic periodic orbit of a map z^2+c_0 can be extended by means of analytic continuation to a multiple-valued algebraic function on the space of all quadratic polynomials z^2+c. Information about the location of the critical points of this function might shed light on the question of possible geometric shapes of hyperbolic components of the Mandelbrot set. I am going to discuss the results of some numerical computations of the critical points of the multipliers. I will also show that as the period of the periodic orbits increases to infinity, the critical points of the multipliers equidistribute on the boundary of the Mandelbrot set.

The talk is based on the joint works with Anna Belova and Tanya Firsova.