Concepedia

SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS

Vladimir I. Arnold

Russian Mathematical Surveys · 1963 · 1.1K citations · 7 references

DOI

Concepts

Abstract

Contents: Perturbation Theory, Adiabatic Invariants, On the Stability of Planetary Motions, Fundamental Theorem, Technical Lemmas, Technique of Smoothing.

References

7

PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN

Vladimir I. Arnold · Russian Mathematical Surveys · 1963 · 939 citations

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On conservation of conditionally periodic motions for a small change in Hamilton's function

A N Kolmogorov · Proceedings of the USSR Academy of Sciences · 1954 · 655 citations

, , +11

A NEW TECHNIQUE FOR THE CONSTRUCTION OF SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS

Jürgen Moser · Proceedings of the National Academy of Sciences · 1961 · 250 citations · Full text

, , +5

AVERAGING IN SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS

V. M. Volosov · Russian Mathematical Surveys · 1962 · 192 citations

, , +12

On the adiabatic theorem for the Hamiltonian system of differential equations in the classical mechanics, I

Takashi Kasuga · Proceedings of the Japan Academy Series A Mathematical Sciences · 1961 · 62 citations · Full text

, , +15