# Liapunov, Aleksandr

**Liapunov, Aleksandr **[Ляпунов, Александр; Ljapunov], b 6 June 1857 in Yaroslavl, Russia, d 3 November 1918 in Odesa. Mathematician and engineer; from 1902 full member of the Imperial Academy of Sciences. Liapunov graduated from Saint Petersburg University in 1880, and from 1885 was a docent and then (1892) professor at Kharkiv University. He was active in the Kharkiv Mathematics Society, as vice-president (1891–8), president (1899–1902), and publications editor. While in Kharkiv Liapunov conducted research in mathematical physics and the theory of probability and obtained important results in both fields. One of his great achievements was the rigorous development of the fundamental concepts of stability theory (now known as the Liapunov-Poincaré theory of stability), which he published in his doctoral dissertation in 1892. In this and succeeding works, he obtained a series of fundamental results on the solution of ordinary linear and nonlinear differential equations. Liapunov’s work ‘Some Questions Connected with the Dirichlet Problem’ (1898) was of great importance to mathematical physics. It investigated the properties of the potential arising from charges and dipoles distributed on a surface, and later led to the study of double-layer potential in the case of dipoles. Liapunov was the first to demonstrate the symmetry of the Green’s function for the Dirichlet problem, and to prove that the solution may be represented by a surface integral. His contributions to probability theory included the introduction and the study of the method of characteristic functions and a general proof of the central limit theorem of probability, which covered much wider conditions than proofs of his predecessors. Liapunov’s scientific work received wide recognition. In 1902 he moved to Saint Petersburg as successor to P. Chebyshev as an academician in applied mathematics.

Wolodymyr Petryshyn

[This article originally appeared in the *Encyclopedia of Ukraine*, vol. 3 (1993).]