Collected Works

1. On the representation of functions of two variables in the form χ[φ(x) + ψ(y)]

2. On functions of three variables

3. The mathematics workshop for schools at Moscow State University

4. The school mathematics circle at Moscow State University: harmonic functions

5. On the representation of functions of several variables as a superposition of functions of a smaller number of variables

6. Representation of continuous functions of three variables by the superposition of continuous functions of two variables

7. Some questions of approximation and representation of functions

8. Kolmogorov seminar on selected questions of analysis

9. On analytic maps of the circle onto itself

10. Small denominators. I. Mapping of the circumference onto itself

11. The stability of the equilibrium position of a Hamiltonian system of ordinary differential equations in the general elliptic case

12. Generation of almost periodic motion from a family of periodic motions

13. Some remarks on flows of line elements and frames

14. A test for nomographic representability using Decartes’ rectilinear abacus

15. Remarks on winding numbers

16. On the behavior of an adiabatic invariant under slow periodic variation of the Hamiltonian

17. Small perturbations of the automorphisms of the torus

18. The classical theory of perturbations and the problem of stability of planetary systems

19. Letter to the editor

20. Dynamical systems and group representations at the Stockholm Mathematics Congress

21. Proof of a theorem of A. N. Kolmogorov on the invariance of quasi-periodic motions under small perturbations of the Hamiltonian

22. Small denominators and stability problems in classical and celestial mechanics

23. Small denominators and problems of stability of motion in classical and celestial mechanics

24. Uniform distribution of points on a sphere and some ergodic properties of solutions of linear ordinary differential equations in a complex region

25. On a theorem of Liouville concerning integrable problems of dynamics

26. Instability of dynamical systems with several degrees of freedom

27. On the instability of dynamical systems with several degrees of freedom

28. Errata to V.I. Arnol’d’s paper: “Small denominators. I.”

29. Small denominators and the problem of stability in classical and celestial mechanics

30. Stability and instability in classical mechanics

31. Conditions for the applicability, and estimate of the error, of an averaging method for systems which pass through states of resonance in the course of their evolution

32. On a topological property of globally canonical maps in classical mechanics

Avainsanat: Mathematics, Partial Differential Equations, Algebra, Theoretical, Mathematical and Computational Physics, Real Functions