The term fractal
usually refers to sets which, in some sense, have a self-similar structure. This
PDF book covers the following topics related to Random Fractals : Representing
fractals by trees, Fine properties of stochastic processes, More on the planar
Brownian path, etc.
Goal of this course
note is primarily to develop the foundations of geometric measure theory, and
covers in detail a variety of classical subjects. A secondary goal is to
demonstrate some applications and interactions with dynamics and metric number
theory.
This note covers the following topics: Rigidity and inflexibility in conformal dynamics, Hausdorff
dimension and conformal dynamics: Strong convergence of Kleinian groups,
Geometrically finite rational maps and Computation of dimension.