Kolmogorov's Heritage in Mathematics

Introduction: Eric Charpentier, Annick Lesne, Nikolaï Nikolski .- The youth of Andrei Nikolaevich and Fourier series: Jean-Pierre Kahane .- Kolmogorov's contribution to intuitionistic logic: Thierry Coquand.- Some aspects of the probabilistic work: Loïc Chaumont, Laurent Mazliak, Marc Yor.- Infinite dimensional Kolmogorov equations: Giuseppe Da Prato.- From Kolmogorov's theorem on empirical distribution to number theory: Kevin Ford.- Kolmogorov's -entropy and the problem of statistical estimation: Mikhail Nikouline, Valentin Solev.- Kolmogorov and topology: Victor M. Buchstaber .- Geometry and approximation theory in A. N. Kolmogorov's works: Vladimir M. Tikhomirov.- Kolmogorov and population dynamics: Karl Sigmund.- Resonances and small divisors: Etienne Ghys.- The KAM Theorem: John H. Hubbard .-From Kolmogorov's Work on Entropy of Dynamical Systems to Non-uniformly Hyperbolic Dynamics: Denis V. Kosygin, Yakov G. Sinai.- From Hilbert's 13th Problem to the theory of neural networks: constructive aspects of Kolmogorov's Superposition Theorem: Vasco Brattka .- Kolmogorov Complexity: Bruno Durand, Alexander Zvonkin.- Algorithmic Chaos and the Incompressibility Method: Paul Vitanyi.

From the reviews:"Andrei N. Kolmogorov (1903-1987) was one of the most prolific and influential mathematicians of the twentieth century. ... this collection would be read by those who hold only a bachelor's degree in mathematics, computer science or physics, and more generally, by those interested in mathematical ideas. ... This impressive collection gives the reader an understanding of the depth and breadth of Kolmogorov's contributions to mathematics. Each chapter includes a substantial list of references that invite further reading." (Elena Anne Marchisotto, MathDL, December, 2007)"The object of Kolmogorov's Heritage in Mathematics is to enable the general mathematical reader (educated to master's level) to grasp something of Kolmogorov's achievements. ... I can judge, it is successful in its aim. ... those mathematicians with a sense of history, who wish to place themselves within the general culture of mathematics, will find this book a worthy memorial to a great man." (T. W. Korner, SIAM reviews, Vol. 50 (4), December, 2008)