# Mathematician:Vladimir Igorevich Arnold

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## Mathematician

Ukrainian mathematician who made important contributions in several areas including dynamical systems theory, catastrophe theory, topology, algebraic geometry, symplectic geometry, differential equations, classical mechanics and singularity theory.

Best known for the Kolmogorov-Arnold-Moser Theorem regarding the stability of integrable systems,

Proved in 1957 that any continuous function of several variables can be constructed with a finite number of two-variable functions, thereby partially solving Hilbert's thirteenth problem.

### Wolf Prize

Vladimir Igorevich Arnold was awarded a Wolf Prize for Mathematics in $\text {2001}$:

*For his deep and influential work in a multitude of areas of mathematics, including dynamical systems, differential equations, and singularity theory.*

## Nationality

Ukrainian

## History

- Born: 12 June 1937 in Odessa, USSR (now Ukraine)
- Died: 3 June 2010 in Paris, France

## Theorems and Definitions

- Kolmogorov-Arnold-Moser Theorem (with Andrey Nikolaevich Kolmogorov and Jürgen Kurt Moser)
- Arnold Diffusion

## Publications

- 1959:
*On mappings of a circle to itself* - 1961:
*On the representation of continuous functions of 3 variables by the superpositions of continuous functions of 2 variables* - 1963:
*Small denominators and stability problems in classical and celestial mechanics* - 1967:
*Problèmes ergodiques de la mécanique classique*(Ergodic Problems of Classical Mechanics) (with A. Avez) - 1971:
*Ordinary Differential Equations* - 1974:
*Mathematical Methods of Classical Mechanics* - 1978:
*Supplementary chapters to the theory of ordinary differential equations* - 1981:
*Singularity theory* - 1982:
*Singularities of differentiable mappings*(Russian) (with A.N. Varchenko and S.M. Gusein-Zade) - 1984:
*Catastrophe theory* - 1988:
*Geometrical Methods In The Theory Of Ordinary Differential Equations* - 1989:
*Huygens and Barrow, Newton and Hooke: Pioneers in mathematical analysis and catastrophe theory from evolvents to quasicrystals* - 1989:
*Contact geometry and wave propagation* - 1990:
*Singularities of caustics and wave fronts* - 1991:
*The theory of singularities and its applications* - 1994:
*Topological invariants of plane curves and caustics* - 1997:
*Lectures on partial differential equations* - 1998:
*On the teaching of mathematics* - 1998:
*Topological methods in hydrodynamics*(with B.A. Khesin) - 1999:
*Bifurcation Theory And Catastrophe Theory*(with Valentin S. Afraimovich) - 2000:
*Arnold problems* - 2001:
*Tsepniye Drobi*(Continued Fractions) - 2007:
*Yesterday and Long Ago*

## Also known as

In Russian: **Влади́мир И́горевич Арно́льд**.