Kolmogorov’s Heritage in Mathematics

• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Άλλοι συγγραφείς: Charpentier, Éric (Επιμελητής έκδοσης), Lesne, Annick (Επιμελητής έκδοσης), Nikolski, Nikolaï K. (Επιμελητής έκδοσης)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007.
• Θέματα: Mathematics.; Dynamics.; Ergodic theory.; Fourier analysis.; Mathematical logic.; Probabilities.; Topology.; Mathematical Logic and Foundations.; Probability Theory and Stochastic Processes.; Dynamical Systems and Ergodic Theory.; Fourier Analysis.

A.N. Kolmogorov (b. Tambov 1903, d. 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 imaginat...

Πίνακας περιεχομένων:

• The youth of Andrei Nikolaevich and Fourier series
• Kolmogorov’s contribution to intuitionistic logic
• Some aspects of the probabilistic work
• Infinite dimensional Kolmogorov equations
• From Kolmogorov’s theorem on empirical distribution to number theory
• Kolmogorov’s ?-entropy and the problem of statistical estimation
• Kolmogorov and topology
• Geometry and approximation theory in A. N. Kolmogorov’s works
• Kolmogorov and population dynamics
• Resonances and small divisors
• The KAM Theorem
• From Kolmogorov’s Work on entropy of dynamical systems to Non-uniformly hyperbolic dynamics
• From Hilbert’s 13th Problem to the theory of neural networks: constructive aspects of Kolmogorov’s Superposition Theorem
• Kolmogorov Complexity
• Algorithmic Chaos and the Incompressibility Method.