Arnold: Swimming Against the Tide by Boris A. Khesin, Serge L. Tabachnikov

By Boris A. Khesin, Serge L. Tabachnikov

Vladimir Arnold, an eminent mathematician of our time, is understood either for his mathematical effects, that are many and well known, and for his powerful critiques, frequently expressed in an uncompromising and galvanizing demeanour. His dictum that "Mathematics is part of physics the place experiments are reasonable" is widely known. This publication comprises components: chosen articles by way of and an interview with Vladimir Arnold, and a set of articles approximately him written via his associates, colleagues, and scholars. The e-book is generously illustrated through a wide number of photos, a few by no means earlier than released. The booklet offers many an aspect of this awesome mathematician and guy, from his mathematical discoveries to his daredevil outside adventures.

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ARNOLD applicable, and I added several pages to my paper of 1959 on the applications of the theory of resonances and structural stability of the mappings of a circle into itself and on small denominators, to the heart beat problem. The paper was sent to Vinogradov’s journal “Izvestiya of the Russian Academy of Sciences” for publication, but was rejected. 9 I was puzzled because I liked it, but Kolmogorov’s reaction was that the heart beat theory, although very interesting, is not of the kind mathematicians should work on.

Then two events happened. The Canadian physiologist Leon Glass discovered that the mathematical theorems on resonances proved in my published paper have applications to heart beat. He published them in a paper and later in a book titled “From Clocks to Chaos”. About the same time Gelfand told me that he was preparing his collected works. “My congratulations, I said, I am very glad”. “Yes, he answered, but I want your paper to be published in it”. I was puzzled, but, since this was not the dangerous genuine collaboration, I gave him the old paper.

By that time, I had already combined the study of degenerations of both kinds and applied them to the planetary motion problem. The results were first presented at the conference on theoretical astronomy held in Moscow on 20–25 November 1961. The conference’s main topic was the artificial satellite motion. I was delighted to meet there and make friends with M. L. Lidov whose students A. I. Neishtadt and M. L. Zieglin later made profound contributions to perturbation theory, averaging, adiabatic invariants, Hamiltonian chaos and materialization of resonances.

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