Fractals in Probability and Analysis - Christopher J Bishop

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Résumé :
A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.

Biographie:
Christopher J. Bishop is a professor in the Department of Mathematics at Stony Brook University, New York. He has made contributions to the theory of function algebras, Kleinian groups, harmonic measure, conformal and quasiconformal mapping, holomorphic dynamics and computational geometry.

Sommaire:
1. Minkowski and Hausdorff dimensions; 2. Self-similarity and packing dimension; 3. Frostman's theory and capacity; 4. Self-affine sets; 5. Graphs of continuous functions; 6. Brownian motion, part I; 7. Brownian motion, part II; 8. Random walks, Markov chains and capacity; 9. Besicovitch?Kakeya sets; 10. The traveling salesman theorem; Appendix A. Banach's fixed-point theorem; Appendix B. Frostman's lemma for analytic sets; Appendix C. Hints and solutions to selected exercises; References; Index.