Vladimir I. Arnold - Collected Works (eBook)

Preface 8
Contents 11
ON THE REPRESENTATION OF FUNCTIONS OF TWO VARIABLES IN THE FORM .[f(x) + .(y)] 14
ON FUNCTIONS OF THREE VARIABLES 18
THE MATHEMATICS WORKSHOP FOR SCHOOLS AT MOSCOW STATE UNIVERSITY 22
The school mathematics circle at Moscow State University: harmonic functions (in Russian) 28
ON THE REPRESENTATION OF FUNCTIONS OF SEVERAL VARIABLES AS A SUPERPOSITION OF FUNCTIONS OF A SMALLER NUMBER OF VARIABLES 38
REPRESENTATION OF CONTINUOUS FUNCTIONS OF THREE VARIABLES BY THE SUPERPOSITION OF CONTINUOUS FUNCTIONS OF TWO VARIABLES 60
SOME QUESTIONS OF APPROXIMATION AND REPRESENTATION OF FUNCTIONS 147
KOLMOGOROV SEMINAR ON SELECTED QUESTIONS OF ANALYSIS 157
ON ANALYTIC MAPS OF THE CIRCLE ONTO ITSELF 162
SMALL DENOMINATORS. I MAPPINGS OF THE CIRCUMFERENCE ONTO ITSELF 165
THE STABILITY OF THE EQUILIBRIUM POSITION OF AHAMILTONIAN SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS IN THE GENERAL ELLIPTIC CASE. 237
GENERATION OF ALMOST PERIODIC MOTION FROM A FAMILY OF PERIODIC MOTIONS 240
SOME REMARKS ON FLOWS OF LINE EL EMENTS AND FRAMES 243
A test for nomographic representability using Decartes’ rectilinear abacus (in Russian) 246
Remarks on winding numbers (in Russian) 249
ON THE BEHAVIOR OF AN ADIABATIC INVARIANT UNDER SLOW PERIODIC VARIATION OF THE HAMILTONIAN 256
SMALL PERTURBATIONS OF THE AUTOMORPHISMS OF THE TORUS 261
THE CLASSICAL THEORY OF PERTURBATIONS AND THE PROBLEM OF STABILITY OF PLANETARY SYSTEMS 266
Letter to the editor (in Russian) 271
Dynamical systems and group representations at the Stockholm Mathematics Congress (in Russian) 272
PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI.PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN 280
Small denominators and stability problems in classical and celestial mechanics (in Russian) 308
SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS 319
UNIFORM DISTRIBUTION OF POINTS ON A. SPHERE AND SOME ERGODIC PROPERTIES OF SOLUTIONS OF LINEAR ORDINARY DIFFERENTIAL EQUATIONS IN A COMPLEX REGION 426
ON A THEOREM OF LIOUVILLE CONCERNING INTEGRABLE PROBLEMS OF DYNAMICS 431
INSTABILITY OF DYNAMICAL SYSTEMS WITH SEVERAL DEGREES OF FREEDOM 436
On the instability of dynamical systems with several degrees of freedom (in Russian) 441
ERRATA TO V. ARNOL’D’S PAPER “SMALL DENOMINATORS. I” 446
Small denominators and the problem of stability in classical and celestial mechanics (in Russian) 448
Stability and instability in classical mechanics (in Russian) 455
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 490
On a topological property of globally canonical maps in classical mechanics. 494
Acknowledgements 500