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Fractals in Probability and Analysis
This PDF book covers the following topics related to Fractals in Probability and Analysis : Minkowski and Hausdorff dimensions, Self-similarity and packing dimension, Frostman’s theory and capacity, Self-affine sets, Graphs of continuous functions, Brownian motion, Random walks, Markov chains and capacity, Besicovitch–Kakeya sets, The Traveling Salesman Theorem.
Author(s): Christopher J. Bishop Stony Brook University, Yuval Peres Microsoft Research
397 Pages
This book is devoted to a phenomenon of fractal sets, or simply fractals. Topics covered includes: Sierpinski gasket, Harmonic functions on Sierpinski gasket, Applications of generalized numerical systems, Apollonian Gasket, Arithmetic properties of Apollonian gaskets, Geometric and group-theoretic approach.
Author(s): A. A. Kirillov
134 Pages
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
Lecture Notes on Fractal Geometry
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Author(s): NA
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