Fractals in the Plane the Ergodic Theory Methods

Overview & Synopsis

This book is an introduction to the theory of iteration of
expanding and nonuniformly expanding holomorphic maps and topics in geometric
measure theory of the underlying invariant fractal sets. Major topics covered:
Basic examples and definitions, Measure preserving endomorphisms, Ergodic theory
on compact metric spaces, Distance expanding maps, Thermodynamical formalism,
Expanding repellers in manifolds and Riemann sphere, preliminaries, Cantor
repellers in the line, Sullivan�s scaling function, application in Feigenbaum
universality, Fractal dimensions, Sullivan�s classification of conformal
expanding repellers, Conformal maps with invariant probability measures of
positive, Lyapunov exponent and Conformal measures.