Kolmogorov's heritage in mathematics

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010184925	QA267.7 K64 2007	Open Access Book	Book	Searching... Unknown
Searching... SPACE Pahang Library	30000003490327	QA267.7 K64 2007	Open Access Book	Book	Searching... Unknown

A.N. Kolmogorov (Tambov 1903, Moscow 1987) was one of the most brilliant mathematicians that the world has ever known. Incredibly deep and creative, he was able to approach each subject with a completely new point of view: in a few magnificent pages, which are models of shrewdness and imagination, and which astounded his contemporaries, he changed drastically the landscape of the subject.

Each chapter treats one of Kolmogorov's research themes, or a subject that was invented as a consequence of his discoveries. The authors present here his contributions, his methods, the perspectives he opened to us, the way in which this research has evolved up to now, along with examples of recent applications and a presentation of the modern prospects.

This book can be read by anyone with a master's (or even a bachelor's) degree in mathematics, computer science or physics, or more generally by anyone who likes mathematical ideas. Rather than presenting detailed proofs, the main ideas are described, and a bibliography for those who wish to understand the technical details.

Eric Charpentier and Annick Lesne and Nikolai NikolskiJean-Pierre KahaneThierry CoquandLoic Chaumont and Laurent Mazliak and Marc YorGiuseppe Da PratoKevin FordMikhail Nikouline and Valentin SolevVictor M. BuchstaberVladimir M. TikhorrarovKarl SigmundEtienne GhysJohn H. HubbardDenis V. Kosygin and Yakov G. SinaiVasco BrattkaBruno Durand and Alexander ZvonkinPaul Vitanyi

Introduction	p. 1
1 The youth of Andrei Nikolaevich and Fourier series	p. 7
2 Kolmogorov's contribution to intuitionistic logic	p. 19
3 Some aspects of the probabilistic work	p. 41
4 Infinite-dimensional Kolmogorov equations	p. 67
5 From Kolmogorov's theorem on empirical distribution to number theory	p. 97
6 Kolmogorov's [epsilon]-entropy and the problem of statistical estimation	p. 109
7 Kolmogorov and topology	p. 139
8 Geometry and approximation theory in A. N. Kolmogorov's works	p. 151
9 Kolmogorov and population dynamics	p. 177
10 Resonances and small divisors	p. 187
11 The KAM Theorem	p. 215
12 From Kolmogorov's work on entropy of dynamical systems to non-uniformly hyperbolic dynamics	p. 239
13 From Hilbert's 13th Problem to the theory of neural networks: constructive aspects of Kolmogorov's Superposition Theorem	p. 253
14 Kolmogorov complexity	p. 281
15 Algorithmic chaos and the incompressibility method	p. 301

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