1. I will present some results about the dependence on the parameter of (numerical value of ) the Hausdorff measure of invariant sets in families of conformal maps. This is a joint work with Tomasz Szarek and Mariusz Urbanski.
  2. In this part of the talk I will recall and discuss the proof (due to M. Tsujii) of the monotonicity of topological entropy in the quadratic family.