Vladimir Igorevich Arnold was a Soviet and Russian mathematician. He is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, and contributed to several areas, including geometrical theory of dynamical systems theory, algebra, catastrophe theory, topology, real algebraic geometry, symplectic geometry, symplectic topology, differential equations, classical mechanics, differential geometric approach to hydrodynamics, geometric analysis and singularity theory, including posing the ADE classification problem.

In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry.