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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, 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.
Author(s): Feliks Przytycki Mariusz Urbanski
324 Pages
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.
Author(s): Curtis T McMullen
NA Pages
This note covers the following topics: Thomasina's Geometry of Irregular Forms, The Chaos Game, The Sierpinski Hexagon, Thomasina's Fern and Valentine's Grouse.
Author(s): Robert L. Devaney
NA Pages
The Fractal Geometry of the Mandelbrot Set, How to Count and How to Add
We are working on the detailed description of this book, we will update this section soon.
Author(s): NA
NA Pages
