Aleksandr Lyapunov was a school friend of Markov and later a student of Chebyshev. He did important work on differential equations, potential theory, stability of systems and probability theory.
His work concentrated on the stability of equilibrium and motion of a mechanical system and the stability of a uniformly rotating fluid. He devised important methods of approximation. Lyapunov's methods, introduced by him in 1899, provide ways of determining the stability of sets of ordinary differential equations.