Cambridge Studies in Advanced Mathematics

Cambridge Studies in Advanced Mathematics

Bishop, Christopher; Peres, Yuval

Cambridge University Press






15 a 20 dias

This book offers a mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities. The clear presentation of a broad range of techniques makes the volume accessible to graduate students, while the independent nature of chapters renders it a useful supplement or resource for a variety of courses.
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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