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Medientyp:
Buch
Titel:
Dimensions, embeddings, and attractors
Enthält:
Machine generated contents note: Preface; Introduction; Part I. Finite-Dimensional Sets: 1. Lebesgue covering dimension; 2. Hausdorff measure and Hausdorff dimension; 3. Box-counting dimension; 4. An embedding theorem for subsets of RN; 5. Prevalence, probe spaces, and a crucial inequality; 6. Embedding sets with dH(X-X) finite; 7. Thickness exponents; 8. Embedding sets of finite box-counting dimension; 9. Assouad dimension; Part II. Finite-Dimensional Attractors: 10. Partial differential equations and nonlinear semigroups; 11. Attracting sets in infinite-dimensional systems; 12. Bounding the box-counting dimension of attractors; 13. Thickness exponents of attractors; 14. The Takens time-delay embedding theorem; 15. Parametrisation of attractors via point values; Solutions to exercises; References; Index.