Vladimir I. Arnold - Collected Works
Representations of Functions, Celestial Mechanics, and KAM Theory 1957-1965
Series: Vladimir I. Arnold - Collected Works; 1;
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Product details:
- Edition number 2010
- Publisher Springer Berlin Heidelberg
- Date of Publication 13 November 2009
- Number of Volumes 1 pieces, Book
- ISBN 9783642017414
- Binding Hardback
- No. of pages487 pages
- Size 244x170 mm
- Weight 1042 g
- Language English
- Illustrations XIII, 487 p. Illustrations, black & white 0
Categories
Table of Contents:
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 sphereand 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.
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