Russian Mathematical Surveys, Volume 18, Number 5, October 1963, 1963

1

THE WORK OF A. N. KOLMOGOROV IN THE THEORY OF PROBABILITY

B V Gnedenko

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https://doi.org/10.1070/RM1963v018n05ABEH004129

9

PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN

V I Arnol'd

View article, PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN PDF, PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN

CONTENTS § 1. Introduction § 2. Formulation of the theorems § 3. Proofs § 4. Technical lemmas § 5. Appendix. The rotatory motion of a heavy asymmetric rigid body References

https://doi.org/10.1070/RM1963v018n05ABEH004130

37

SOME REMARKS ON THE SPECTRAL PROPERTIES OF ERGODIC DYNAMICAL SYSTEMS

Yakov G Sinai

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https://doi.org/10.1070/RM1963v018n05ABEH004131

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KOLMOGOROV'S WORK ON

-ENTROPY OF FUNCTIONAL CLASSES AND THE SUPERPOSITION OF FUNCTIONS

V M Tikhomirov

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CONTENTS § 1. Introduction § 2. What is entropy and -entropy? § 3. Which are more numerous-differentiable functions or analytic functions? § 4. The number of variables and the massiveness of function spaces § 5. Can one get along without continuous functions of several variables? § 6. A lecture by Kolmogorov

https://doi.org/10.1070/RM1963v018n05ABEH004132

89

ON THE LAWS OF SMALL-SCALE TURBULENT FLOW OF LIQUIDS AND GASES

A S Monin and A M Yaglom

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https://doi.org/10.1070/RM1963v018n05ABEH004133

111

A. N. KOLMOGOROV AS A TEACHER

P S Aleksandrov and B V Gnedenko

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https://doi.org/10.1070/RM1963v018n05ABEH004134

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