Mathematics Books Fractals Books

Fractals in the Plane the Ergodic Theory Methods

Fractals in the Plane the Ergodic Theory Methods

Fractals in the Plane the Ergodic Theory Methods

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, Sullivanís scaling function, application in Feigenbaum universality, Fractal dimensions, Sullivanís classification of conformal expanding repellers, Conformal maps with invariant probability measures of positive, Lyapunov exponent and Conformal measures.

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s324 Pages
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