- 12-81 Vladimir I. Arnold
- From superpositions to KAM theory
Aug 2, 12
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Abstract. V. I. Arnold (1937-2010) published several articles where he described, in the form of recollections, his two earliest research problems (superpositions of continuous functions and quasi-periodic motions in dynamical systems), the main results and their interrelations. Of these articles, the first exposition (V. I. Arnold, From superpositions to KAM theory. In: Vladimir Igorevich Arnold. Selected-60. PHASIS, Moscow, 1997, pp. 727-740, in Russian) has never been translated into English; however, it contains many details absent in the subsequent articles. It seems therefore that publishing the English translation of Arnold's 1997 exposition would not be superfluous. The present paper is this translation prepared by M. B. Sevryuk. A related material is contained also in Arnold's recollections "On A. N. Kolmogorov". Slightly different versions of these reminiscences were published several times in Russian and English as well.