Aleksandr Lyapunov (nonfiction)

Aleksandr Lyapunov.

Aleksandr Mikhailovich Lyapunov (Russian: Алекса́ндр Миха́йлович Ляпуно́в, pronounced [ɐlʲɪkˈsandr mʲɪˈxajləvʲɪtɕ lʲɪpʊˈnof]; June 6 [O.S. May 25] 1857 – November 3, 1918) was a Russian mathematician, mechanician and physicist. His surname is sometimes romanized as Ljapunov, Liapunov, Liapounoff or Ljapunow. He was the son of astronomer Mikhail Lyapunov and the brother of pianist and composer Sergei Lyapunov.

Lyapunov is known for his development of the stability theory of a dynamical system, as well as for his many contributions to mathematical physics and probability theory.

A major theme in Lyapunov's research was the stability of a rotating fluid mass with possible astronomical application. This subject was proposed to Lyapunov by Pafnuty Chebyshev as a topic for his masters thesis which he submitted in 1884 with the title On the stability of ellipsoidal forms of rotating fluids. This led on to his 1892 doctoral thesis The general problem of the stability of motion. The thesis was defended in Moscow University on September 12, 1892, with Nikolai Zhukovsky and V. B. Mlodzeevski as opponents.

Lyapunov contributed to several fields, including differential equations, potential theory, dynamical systems and probability theory.

His main preoccupations were the stability of equilibria and the motion of mechanical systems, 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 equation of Laplace.

In the theory of potential, his work from 1897 On some questions connected with 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 dynamic 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 functions he used for the proof later found widespread use in probability theory.

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 theater, 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 Academy of Sciences in Paris.

Lyapunov's impact was significant, and a number of different mathematical concepts therefore bear his name:

• Lyapunov equation
• Lyapunov exponent
• Lyapunov function
• Lyapunov fractal
• Lyapunov stability
• Lyapunov's central limit theorem
• Lyapunov vector

Nonfiction cross-reference

• Andrey Markov
• Laplace's equation (nonfiction)
• Dirichlet problem (nonfiction)
• Mathematician (nonfiction)
• Mikhail Lyapunov (nonfiction) - Brother
• Nikolay Yegorovich Zhukovsky (nonfiction)
• Pafnuty Chebyshev (nonfiction) - Doctoral advisor
• V. B. Mlodzeevski (nonfiction)
• Vladimir Steklov (nonfiction) - Doctoral student

External links:

• Aleksandr Lyapunov @ Wikipedia