Collected Works Representations of Functions, Celestial Mechanics and KAM Theory, 1957–1965 /

• Main Author: Arnold, Vladimir I. (Author)
• Corporate Author: SpringerLink (Online service)
• Other Authors: Givental, Alexander B. (Editor), Khesin, Boris A. (Editor), Marsden, Jerrold E. (Editor), Varchenko, Alexander N. (Editor), Vassiliev, Victor A. (Editor), Viro, Oleg Ya (Editor), Zakalyukin, Vladimir M. (Editor)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Series: Vladimir I. Arnold - Collected Works ; 1
• Subjects: Mathematics.; Algebra.; Partial differential equations.; Functions of real variables.; Physics.; Partial Differential Equations.; Theoretical, Mathematical and Computational Physics.; Real Functions.

 On the representation of functions of two variables in the form ?[?(x) + ?(y)] -- On functions of three variables -- The mathematics workshop for schools at Moscow State University -- The school mathematics circle at Moscow State University: harmonic functions -- On the representation of functions of several variables as a superposition of functions of a smaller number of variables -- Representation of continuous functions of three variables by the superposition of continuous functions of two variables -- Some questions of approximation and representation of functions -- Kolmogorov seminar on selected questions of analysis -- On analytic maps of the circle onto itself -- Small denominators. I. Mapping of the circumference onto itself -- The stability of the equilibrium position of a Hamiltonian system of ordinary differential equations in the general elliptic case -- Generation of almost periodic motion from a family of periodic motions -- Some remarks on flows of line elements and frames -- A test for nomographic representability using Decartes’ rectilinear abacus -- Remarks on winding numbers -- On the behavior of an adiabatic invariant under slow periodic variation of the Hamiltonian -- Small perturbations of the automorphisms of the torus -- The classical theory of perturbations and the problem of stability of planetary systems -- Letter to the editor -- Dynamical systems and group representations at the Stockholm Mathematics Congress -- Proof of a theorem of A. N. Kolmogorov on the invariance of quasi-periodic motions under small perturbations of the Hamiltonian -- Small denominators and stability problems in classical and celestial mechanics -- Small denominators and problems of stability of motion in classical and celestial mechanics -- Uniform distribution of points on a sphere and some ergodic properties of solutions of linear ordinary differential equations in a complex region -- On a theorem of Liouville concerning integrable problems of dynamics -- Instability of dynamical systems with several degrees of freedom -- On the instability of dynamical systems with several degrees of freedom -- Errata to V.I. Arnol’d’s paper: “Small denominators. I.” -- Small denominators and the problem of stability in classical and celestial mechanics -- Stability and instability in classical mechanics -- 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 -- On a topological property of globally canonical maps in classical mechanics.