Editing Aleksandr Lyapunov (section)

== Work ==
[[File:Aleksandr Lyapunov.jpg|thumb|Aleksandr Lyapunov in 1908]]
Lyapunov contributed to several fields, including [[differential equation]]s, [[potential theory]], [[dynamical system]]s and [[probability theory]]. His main preoccupations were the stability of equilibria and the motion of mechanical systems, especially rotating fluid masses, and the study of particles under the influence of gravity. His work in the field of [[mathematical physics]] regarded the boundary value problem of the [[Laplace's equation|equation of Laplace]]. In the theory of potential, his work from 1897 ''On some questions connected with [[Peter Gustav Lejeune Dirichlet|Dirichlet's]] problem'' clarified several important aspects of the theory. His work in this field is in close connection with the work of Steklov. Lyapunov developed many important approximation methods. His methods, which he developed in 1899, make it possible to define the stability of sets of ordinary differential equations. He created the modern theory of the stability of a dynamical system. In the theory of probability, he generalized the works of Chebyshev and Markov, and proved the [[Central Limit Theorem]] under more general conditions than his predecessors. The method of [[characteristic function]]s he used for the proof later found widespread use in probability theory.{{sfn|Smirnov|1992}}

Like many mathematicians, Lyapunov preferred to work alone and communicated mainly with few colleagues and close relatives. He usually worked late, four to five hours at night, sometimes the whole night. Once or twice a year he visited the theatre, or went to some concert. He had many students. He was an honorary member of many universities, an honorary member of the academy in Rome and a corresponding member of the [[French Academy of Sciences|Academy of Sciences]] in Paris.{{sfn|Smirnov|1992}}

Lyapunov's impact was significant, and the following mathematical concepts are named after him: 
* [[Lyapunov equation]]
* [[Lyapunov exponent]]
* [[Lyapunov function]]
* [[Lyapunov fractal]]
* [[Lyapunov stability]]
* [[Lyapunov's central limit theorem]]
* [[Lyapunov vector]]