James C. Robinson is Professor of Mathematics at Warwick University.
Inhaltsangabe
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.
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.
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