Aleksandr Mikhailovich Lyapunov

Aleksandr Mikhailovich Lyapunov (06.06.1857-03.11.1918), Russian mathematician and engineer, Professor (1892), academician Petersburg AN (1901), an outstanding representative of the St. Petersburg mathematical school, established L. L. Chebyshev. Tsp. St. Petersburg, Kharkov and Kazan University comrade, a foreign member of. Accademia dei Lincei, Corresponding Member. Paris Academy of Sciences, foreign member of. Mathematical Circle of Palermo, an honorary member of. Kharkov Mathematical Islands, etc.. research on in -. Genus. Yaroslavl. In 1876 he entered the natural separation of physical and mathematical faculty of St. Petersburg University Press, which at that time worked D. I. Mendeleev, P. L. Chebyshev, D. K. Bobylev, A. N. Evgeniya, E. I. Zolotarev etc.. eminent representatives of science and culture. Lectures II. L. Chebyshev produced by A. impression that a month later, he moved with a natural branch of mathematical. At the 4 th year Zap, he was awarded a gold medal for the development proposed by the Faculty theme 'On the equilibrium of solid bodies in a heavy fluid'. In 1880 he graduated brilliantly un-t and was left with him to prepare for a professorship at the Department of Mechanics. Scientific activities L. was varied. He is the creator of the theory of stability of motion, and the author of fundamental studies of equilibrium figures of rotating fluid. What is important is the contribution of L. in probability theory, and his research on the potential theory have opened new avenues for the development of methods of mathematical physics. Successfully defended his thesis for a master's degree in applied mathematics at the theme 'On the stability of ellipsoidal forms of equilibrium of a rotating fluid', A. moved to Kharkov Univ. In the 1888-1892 published several articles devoted to solving the problem of stability of motion of material systems, which reduces to the study of systems of differential equations. The problem of stability of motion belongs to the category of difficult problems of natural. She studied by many outstanding mathematicians of M. Lagrange to A. Poincare. In this paper, 'The general problem of stability of motion' (1892) A. proposed new general rigorous methods for solving problems of stability of motion. One of these methods, based on the notion of t. n. Lyapunov function, enabled him to obtain important for its application of the criterion of stability solutions. L Creations. research methods successfully applied in others. sections of the theory of differential equations. Have great contribution of L. and in mathematical physics, particularly in theory-building. Especially important is his memoir 'On some issues relating to the Dirichlet problem' (1898). In 1902, the scientist moved to St. Petersburg and returns to the scientific work. The first work of the Petersburg period of L. devoted lezhandrovskoy Laplace and hydrostatic theory of figures of planets. In 1905, he again begins to deal with the problems of equilibrium figures of a homogeneous fluid, which are formed under the influence of uniform rotation around a constant axis. In particular, L. proved the instability of a so-called. pear-shaped figures and thus refutes the opposite erroneous assertion of the English astronomer J. Darwin. L. made important contributions to the theory of probability, giving a simple and rigorous proof of the central limit theorem in a more general form than the one in which she addressed to him P. L. Chebyshev and L. L. Markov. To prove his theorem L. developed an original and very fruitful method of characteristic functions, which is widely used in the modern theory of probability.