Vladimir Igorevich Arnold is one of the most influential mathematicians
of our time. V. I. Arnold launched several mathematical domains (such as
modern geometric mechanics, symplectic topology, and topological fluid
dynamics) and contributed, in a fundamental way, to the foundations and
methods in many subjects, from ordinary differential equations and
celestial mechanics to singularity theory and real algebraic geometry.
Even a quick look at a partial list of notions named after Arnold
already gives an overview of the variety of such theories and domains:
KAM (Kolmogorov Arnold Moser) theory, The Arnold conjectures in
symplectic topology, The Hilbert Arnold problem for the number of zeros
of abelian integrals, Arnold s inequality, comparison, and
complexification method in real algebraic geometry, Arnold Kolmogorov
solution of Hilbert s 13th problem, Arnold s spectral sequence in
singularity theory, Arnold diffusion, The Euler Poincare Arnold
equations for geodesics on Lie groups, Arnold s stability criterion in
hydrodynamics, ABC (Arnold Beltrami Childress) ?ows in ?uid dynamics,
The Arnold Korkina dynamo, Arnold s cat map, The Arnold Liouville
theorem in integrable systems, Arnold s continued fractions, Arnold s
interpretation of the Maslov index, Arnold s relation in cohomology of
braid groups, Arnold tongues in bifurcation theory, The Jordan Arnold
normal forms for families of matrices, The Arnold invariants of plane
curves. Arnold wrote some 700 papers, and many books, including 10
university textbooks. He is known for his lucid writing style, which
combines mathematical rigour with physical and geometric intuition.
Arnold s books on Ordinarydifferentialequations and Mathematical
methodsofclassicalmechanics became mathematical bestsellers and integral
parts of the mathematical education of students throughout the world."
