Vladimir I. Arnol’d (1937–2010)

By Hinke Osinga

Vladimir Igorevich Arnol'd

Vladimir Igorevich Arnol'd, born in Odessa, Ukraine (then part of the USSR), was awarded the Candidate's Degree (equivalent to a PhD) from Moscow State University in 1961, when he was only 19 years old. In his thesis he completed the proof of Hilbert's 13th Problem. He subsequently joined Moscow State University in 1961, became Professor of Mechanics there in 1965, and remained until 1986. He then took up a position at the Steklov Institute of Mathematics in Moscow. From 1993 until 2005 he was also Professor at the University Paris-Dauphine in France, spending spring and summer in Paris, fall and winter in Moscow. He was a member of the Russian Academy of Sciences and foreign member of the Academy of Sciences in Britain, France, Italy and the USA. Arnold has been awarded many prestigious prizes, including the Wolf Prize in 2001 "for his deep and influential work in a multitude of areas of mathematics, including dynamical systems, differential equations and singularity theory."

Arnol'd was an influential mathematician with a broad as well as deep mathematical interest. He is famous in the dynamical system's community for his fundamental work on catastrophe theory and variational equations. Arnol'd is the "A" of KAM theory (with Andrey Kolmogorov, his PhD advisor, and Jürgen Moser), and he discovered what is now known as Arnol'd diffusion; see "Instability of dynamical systems with several degrees of freedom" [Sov. Math. Doklady 5 (1964)]. Many of us were introduced to dynamical systems via his classic books Mathematical Methods of Classical Mechanics (Springer-Verlag, 1989) and Geometrical Methods In The Theory Of Ordinary Differential Equations (Springer-Verlag, 1988). For example, the Arnol'd circle map, explaining the organization of periodic and quasiperiodic motion by Arnol'd tongues, is a standard topic of introductory courses on dynamical systems.

See also the story My lunch with Arnol'd in the April 2007 issue of DSWeb Magazine


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