Collected Works

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

Chapter 2 On functions of three variables

Chapter 3 The mathematics workshop for schools at Moscow State University

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

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

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

Chapter 7 Some questions of approximation and representation of functions

Chapter 8 Kolmogorov seminar on selected questions of analysis

Chapter 9 On analytic maps of the circle onto itself

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

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

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

Chapter 13 Some remarks on flows of line elements and frames

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

Chapter 15 Remarks on winding numbers

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

Chapter 17 Small perturbations of the automorphisms of the torus

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

Chapter 19 Letter to the editor

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

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

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

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

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

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

Chapter 26 Instability of dynamical systems with several degrees of freedom

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

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

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

Chapter 30 Stability and instability in classical mechanics

Chapter 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