The General Theory of Dynamical Systems and Classical Mechanics

Abstract

It was a surprise to me that I would have to present a paper at the final session of the Congress in this large hall, which had been known to me rather as a place for the performance of great musical compositions of the world conducted by Mengelberg. The paper which I have prepared, without taking into account that it would occupy such an honourable position in the programme of the Congress, is devoted to a rather special range of problems. My aim is to elucidate ways of applying basic concepts and results in the modern general metrical and spectral theory of dynamical systems to the study of conservative dynamical systems in classical mechanics. However, it seems to me that the subject I have chosen may also be of broader interest, as one of the examples of the appearance of new, unexpected and profound relationships between different branches of classical and modern mathematics.