Aleksandr lyapunov biography of william

He taught at the university but in the spring of his wife's health began to deteriorate rapidly. Natalia Rafailovna suffered from a form of tuberculosis and Lyapunov was greatly disturbed to watch her health fail. On 31 October Lyapunov's wife died and later that day Lyapunov shot himself. He died three days later in hospital. We have described Lyapunov's main work which was on the theory of rotating liquids.

There are, however, other aspects of his work we should mention. One is certainly his contributions to probability which he became interested in because of courses he was teaching on that subject. In particular in two papers published in andhe proved the central limit theorem using a technique based on characteristic functions. Another contribution which we should mention is that as editor for two volumes of Euler's collected works.

He was honoured for his outstanding contributions by election to various academies such as the Accademia dei Lincei and the French Academy of Sciences He was also given honorary membership of the universities of St Petersburg, Kharkov and Kazan. Various tributes were paid to him on the centenary of his birth. The text of this lecture is given in [ 22 ].

Other papers such as [ 8 ] describe the way that Lyapunov's contributions to the stability of motion has influenced the development of the subject over a long period of time. Topics considered in [ 8 ] include: stability, particularly the stability of critical points; the construction and the application of the Lyapunov function; stability of functional- differential equations ; the second Lyapunov method; and the method of the Lyapunov vector function in stability theory and nonlinear analysis.

Lyapunov equation Lyapunov exponent Lyapunov fractal Lyapunov function Lyapunov stability Lyapunov time Lyapunov's central limit theorem Lyapunov's condition Lyapunov—Malkin theorem Lyapunov—Schmidt reduction. Notes [ edit ]. His surname is variously romanized as LjapunovLiapunovLiapounoff or Ljapunow. References [ edit ]. Lyapunov The general problem of the stability of motion.

Aleksandr lyapunov biography of william

Kharkov: Kharkov Mathematical Society. Further reading [ edit ]. Lyapunov, A. Smith: Automatica vol. Lyapunov's work", International Journal of Control55 3 : —doi : External links [ edit ]. Wikimedia Commons has media related to Aleksandr Lyapunov. Chaos theory. Bifurcation theory Control of chaos Dynamical system Ergodic theory Quantum chaos Stability theory Synchronization of chaos.

Yorke Lai-Sang Young. Multifractal system. Fractal canopy Space-filling curve H tree. Buddhabrot Orbit trap Pickover stalk. Authority control databases. IdRef Encyclopedia of Modern Ukraine. Toggle the table of contents. Aleksandr Lyapunov. Saint Petersburg State University. Lyapunov function Lyapunov stability Lyapunov exponent Lyapunov central limit theorem Lyapunov vector Qualitative theory of differential equations.

Scientific career. Here, the cases when the characteristic equation has one root equal to zero, or when it has two purely imaginary conjugate roots, are of special interest; these cases were exhaustively investigated by Lyapunov. In the case of periodic coefficients Lyapunov examined the possibilities arising in two especially interesting instances: when one of the roots of the characteristic equation is equal to unity and when two imaginary conjugate roots have a modulus equal to unity.

Among many other results is the proof of the theorem of the instability of motion if the force function of the forces acting on the system is not a maximum. Specific results obtained by both these scholars coincide, but they do not deal with the basic content or the basic methods of their works. Problems of stability arise in the determination of the work regimen of various machines, in the construction of airplanes, electrical engineeringand ballistics.

Lyapunov studied figures of equilibrium of a uniformly rotating liquid over a period of thirty-six years. According to a well-known hypothesis, each such body was initially in a liquid state; it took its present form before solidification, having previously received an unchanging form as the result of internal friction. Lyapunov mentioned the mathematical difficulty of studying equilibrium figures, a study which entails the solution of nonlinear integral equations.

Later, Jacobi demonstrated that certain triaxial ellipsoids could also be such figures. Other scholars also studied this problem. When, inChebyshev placed before Lyapunov the question concerning the possibility of the existence of other equilibrium figures that are close to ellipsoidal, Lyapunov could solve the problem only in the first approximation.

Believing it impossible to judge the existence of new figures according to the first approximation, he put off definitive solution to the question. On the other hand, in this thesis he examined the problem of the stability of the Mac-laurin and Jacobi ellipsoids, injecting clarity and rigor into the statement of the problem, defining for the first time the concept of stability for a continuous medium.

A number of methods are entailed in the consistent determination the equations of these figures. In solving all these problems and the corresponding nonlinear integral and integral-differential equations, Lyapunov had to overcome great mathematical difficulties. To this end he devised delicate methods of approximation, the convergence of which he proved with the rigor of contemporary mathematics; generalized the concept of the integral in the direction of the Stieltjes-Riemann integral ; and proved a number of new theorems on spherical functions.

The astronomer G. Darwin encountered the problem of the stability of pear-shaped forms in his hypothesis concerning the origin of double stars arising from the division of a rotating liquid mass into two bodies. These investigations created the foundation of a number of classic methods for solving boundary-value problems. Chebyshev gave the first such generalization of this theorem inindicating the possibility of its proof, in the form given by him, by the method of moments; and Markov carried out the full proof on this basis in These works by Lyapunov also served as the starting point for many later investigations.

Original Works. Lukomskaya, V, I. Smirnov, ed. Moscow-Leningrad, Collections of his writings are A. Moscow,which includes Russian translations of all works written in French. Petersburg, Secondary Literature. In probability theory he generalised the works of Chebyshev and Markov and he finally proved the Central limit theorem using more common conditions than his forerunners.

The method he used for the proof is today one of the foundations of probability theory. From to he was a head of Kharkov mathematical society and an editor of his News. On the December 2, he was elected as a corresponding member of the Russian Academy of Sciences, and on the October 6, as a fully entitled member of the Academy in the field of applied mathematics.

With his researches on celestial mechanics he opened a new page in the history of global aleksandr lyapunov biography of william and he showed the inaccuracy in the knowledge of several foreign scientists. In he participated at the 4th Mathematical congress in Rome. At this time he took part in the publication of Euler's selected works, and he was an editor of the 18th and 19th part of this miscellany.

By the end of June he went with his wife, who was seriously ill, to his brother Boris in Odessa, Russia now Ukraine. His wife's impending death, his own partial blindness, and the generally bad conditions for life, all contributed to his anxiety. In spite of this he delivered his last lecture about the form of celestial bodies at the invitation of the Department of Physics and Mathematics at Odessa.

On October 31 his wife died, and on the same day he shot himself. He then lay unconscious a few days till his death. He usually worked four to five hours at night, and many times even the whole night. Once or twice he visited the theatre or he went to some concert. He had many students. But for the few who really knew him, Lyapunov was a rather raptured man.

He had a lean figure, outwardly he acted pretty rude, otherwise he had a hot-blooded and sensitive temper. He was an honorary member of many universities, an external member of the Academy in Rome and a corresponding member of the Academy of Sciences in Paris. Physics Encyclopedia.