A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
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.
Inhaltsangabe
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.
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.
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