2007

Kolmogorov’s Heritage in Mathematics

Editors:

ISBN: 978-3-540-36349-1 (Print) 978-3-540-36351-4 (Online)

Table of contents (15 chapters)

  1. Front Matter

    Pages I-VIII

  2. No Access

    Book Chapter

    Pages 7-18

    The youth of Andrei Nikolaevich and Fourier series

  3. No Access

    Book Chapter

    Pages 19-40

    Kolmogorov’s contribution to intuitionistic logic

  4. No Access

    Book Chapter

    Pages 41-66

    Some aspects of the probabilistic work

  5. No Access

    Book Chapter

    Pages 67-96

    Infinite dimensional Kolmogorov equations

  6. No Access

    Book Chapter

    Pages 97-108

    From Kolmogorov’s theorem on empirical distribution to number theory

  7. No Access

    Book Chapter

    Pages 109-137

    Kolmogorov’s ε-entropy and the problem of statistical estimation

  8. No Access

    Book Chapter

    Pages 139-150

    Kolmogorov and topology

  9. No Access

    Book Chapter

    Pages 151-176

    Geometry and approximation theory in A. N. Kolmogorov’s works

  10. No Access

    Book Chapter

    Pages 177-186

    Kolmogorov and population dynamics

  11. No Access

    Book Chapter

    Pages 187-213

    Resonances and small divisors

  12. No Access

    Book Chapter

    Pages 215-238

    The KAM Theorem

  13. No Access

    Book Chapter

    Pages 239-252

    From Kolmogorov’s Work on entropy of dynamical systems to Non-uniformly hyperbolic dynamics

  14. No Access

    Book Chapter

    Pages 253-280

    From Hilbert’s 13th Problem to the theory of neural networks: constructive aspects of Kolmogorov’s Superposition Theorem

  15. No Access

    Book Chapter

    Pages 281-299

    Kolmogorov Complexity

  16. No Access

    Book Chapter

    Pages 301-317

    Algorithmic Chaos and the Incompressibility Method