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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
Lectures On Fractals And Dimension Theory
This note covers the following topics: Basic Properties and Examples, Iterated Function Schemes, Computing dimension, Some Number Theory and algorithms, Measures and Dimension, Classic results: Projections, Slices and translations, Tranversality and Iterated function schemes with overlaps.
Author(s): Mark Pollicott
106 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
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