Random Complex Dynamics

During recent years there has been growing interest in random dynamical systems, in particular-random conformal dynamics. I will start with quick introduction about real one-dimensional dynamics, and then pass to conformal random dynamical systems. Necessary basic concepts of conformal dynamics will be explained. The subjects will include:

  1. random circle homeomorphisms- a short introduction to the subject
  2. random measures in Polish spaces
  3. random iterations of polynomials, connectedness of the random Julia set, harmonic measure on the random Julia set
  4. random conformal repellers; dimension of random conformal repellers; dependence on parameters
  5. random transcendental functions- a short outline