Alexander Mikhailovich Lyapunov

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Alexander Mikhailovich Lyapunov

Aleksandr Lyapunov ( Russian Александр Михайлович Ляпунов ., Scientific transliteration Aleksandr Michajlovič Ljapunov ; born May 25 . Jul / 6. June  1857 greg. In Yaroslavl , † 3. November 1918 in Odessa ) was a Russian mathematician and physicist . Common spellings are also Ljapunov, Ljapunoff or (especially in English) Lyapunov and Liapunov.

parents house

Lyapunov's father, Mikhail Wassiljewitsch Lyapunow (1820–1868) was a well-known astronomer and director of the Yaroslavl Demidowski Lyceum. Because of the reaction of the university administration to the departure of Lobachevsky , he completely gave up his activity at the observatory of the Kazan University in 1864. He and his family moved to the property of his wife in the Simbirsk governorate , where he devoted his time to teaching his eldest sons, Alexander and Sergej (1859-1924). Sergei and another son, Boris, later embarked on a career as a composer. The father spent the long winter evenings with the sons and taught them with the help of games on maps all over the world. He owned many books in Russian, German and French on mathematics, astronomy, philosophy, history, ethnography, political economy and literature. After the sudden death of his father, Alexander was tutored by his uncle RM Setschenow ( Russian : P. М. Сеченов ), brother of the famous physiologist Ivan Mikhailovich Sechenov . There he was taught together with his cousin, his future wife Natalja Rafailovna. In 1870 his mother moved with her sons to Nizhny Novgorod , where he attended high school from the third grade onwards, which he graduated with honors in 1876.

Career

Lyapunov studied at the physical-mathematical faculty of the University of Saint Petersburg ; there was Andrei Markov , a fellow student of his and a close friend. At first he attended Mendeleev's lectures on chemistry. After a month he switched to mathematics, but continued to attend chemistry classes. His professors in mathematics included Chebyshev and his students Alexander Nikolayevich Korkin and Yegor Ivanovich Solotarev . Lyapunov wrote his first independent work under the guidance of the mechanics professor Dmitri Konstantinowitsch Bobylew (1842-1917). In the fourth year of his studies he won a gold medal for a thesis in hydrostatics at the suggestion of the faculty. This work was the basis of its initial release the balance of heavy bodies in heavy liquids which are found in containers of certain form About ( О равновесии тяжелых тел в тяжелых жидкостях, содержащихся в сосуде определенной формы ) and about the potential of hydrostatic pressure ( О потенциале гидростатических давлений ). In both papers he used many new approaches and developed new rigorous proofs for some previously incomplete theorems of hydrostatics. With the first thesis he achieved the title of "candidate in mathematical sciences", which corresponds to the German doctorate. Now he was able to leave the university to prepare for the appointment to the professorship.

In 1882 he successfully passed the master’s exam and later, in 1885, he obtained his master’s degree in applied mathematics with the dissertation on the stability of elliptical equilibrium forms of rotating liquids. ( Об устойчивости эллипсоидальных форм равновесия вращающейся жидкости ). This thesis dealt with an important and difficult problem to understand the shape of rotating liquids, the question of whether new equilibrium figures appear at high rotation speeds at which the ellipsoid as an equilibrium figure became unstable. Chebyshev had offered Solotarev and Sofya Kovalevskaya the same job , and Chebyshev was aware of their difficulty. Vladimir Andreyevich Steklov , a student of Lyapunov and later a member of the Academy of Sciences, remarked, "Chebyshev saw such immense research potential in the young man that he dared to entrust him with such arduous work." Lyapunov had at the Worked for two years and it earned him immediate international recognition.

In 1885 he became a private lecturer at the Kharkov University at the Mechanics Department, where he replaced WG Imzhenetsky, who had been elected a member of the Russian Academy of Sciences . Lyapunov had given lectures at the Mechanics Chair since 1880 and had spent a lot of time on them. Steklow said of his lectures:

“ A handsome young man, almost like the other students in appearance, entered the auditorium with the old dean, Professor Lewakowski, who was respected by all students. After the dean left, the young man, his voice trembling, began his lecture on a subject on the dynamics of the point instead of the subject on the dynamics of systems. This subject was already included in Professor Delarju's lectures. I was in fourth grade. I had heard the lectures in Moscow by Dawidow, Zinger, Soletow and Orlov. I had also been at Kharkov University for two years, so I was familiar with the mechanics lectures. But I didn't know the subject from the start and I had never seen it in a textbook. So the boredom during the lecture was completely gone. Alexander Michailowitsch achieved in one hour - without knowing it himself - the respect of the audience with the force of a natural talent, as one has seldom seen in such youth. From that day on, the students looked at him differently and showed him special respect. Often they didn't even dare speak to him so as not to show their ignorance. "

Lyapunov taught at the university special courses on theoretical mechanics, integration of differential equations and probability theory . These lectures were never published, but are passed down through student records. He taught mechanics in six subjects: kinematics , dynamics of point masses , dynamics of point mass systems, theory of attractive forces, theory of deformation of solid bodies and hydrostatics . At the same time he taught analytical mechanics between 1887 and 1893 at the Technical University of Kharkov.

He received his doctorate in science (habilitation) in 1892 with the dissertation A general task for the stability of a movement ( Общая задача об устойчивости движения ). One of the reviewers was Nikolai Jegorowitsch Schukowski , one of the founders of the ZAGI , who had already defended a dissertation on the same topic ten years earlier. After completing his doctorate, Lyapunov became a full professor at Kharkov University. After Chebyshev's death in 1894, he became full professor for the chair of applied mathematics at St. Petersburg University in 1901, where he devoted himself entirely to teaching and research.

In 1908 he took part in the fourth Mathematical Congress in Rome . At that time he was working on the complete edition of Euler's works and was the editor of the 18th and 19th volumes of this edition. In 1916 he was elected a corresponding member of the Académie des Sciences in Paris. At the end of June 1917 he went with his seriously ill wife to his brother Boris in Odessa . The threatened death of his wife, his own visual impairment and the generally poor living conditions led to his depression . Nevertheless, he gave his last lecture in September 1918 on the equilibrium form of celestial bodies at the invitation of the Faculty of Physics and Mathematics in Odessa. His wife died on October 31, and he tried to shoot himself on the same day. He was in a coma for a few days before he died.

He usually worked four to five hours a night, and often all night. Once or twice a year he went to the theater or he went to a concert. He had a lot of students. For those who knew little about him, Lyapunov was a rather reserved person. He had a slim figure, outwardly he sometimes looked quite rough, on the other hand he had a hot-blooded and sensitive temperament.

He corresponded with Henri Poincaré , Jacques Hadamard , Heinrich Burkhardt , Camille Jordan , Paul Appell , Pierre Duhem and Vito Volterra , among others .

plant

He has done significant work in the fields of mechanics and mathematical physics, differential equations , potential theory , the stability of dynamic systems and their equilibrium points, and probability theory .

His 1898 work On Some Questions, Linked to Dirichlet's Problems ( О некоторых вопросах, связанных с задачей Дирихле ) contains a study of the properties of the potential around charges and dipoles that are continuously distributed on any surface. His work in this area is closely related to that of Steklow. Lyapunov developed many important approximation methods. His methods, which he developed in 1889, today known as Lyapunov methods , allow the stability of solutions to ordinary differential equations to be defined and investigated. He worked out the modern strict theory of the stability of the movement of a mechanical system with a finite number of parameters. In probability theory, he generalized the results of Chebyshev and Markov and finally proved the Central Limit Theorem ( Lyapunov theorem ) under less special conditions than his predecessors ( Lyapunov condition ). The method he used is one of the foundations of probability theory today.

Honors and memberships

From 1899 to 1902 he was chairman of the Kharkov Mathematical Society and an editor of its communications . On December 2, 1900 he was elected a corresponding member of the Russian Academy of Sciences and on October 6, 1901 a full member of the Academy for the Field of Applied Mathematics. He was honorary doctor in Kharkiv, St. Petersburg and Kazan, foreign member of the Accademia dei Lincei (1909) and corresponding member of the Academy of Sciences in Paris (1916).

The lunar crater Lyapunov and the asteroid (5324) Lyapunov are named after him.

Fonts

  • Selected works (Russian), Moscow, Leningrad 1948
  • Collected works (Russian, also Russian translation of the articles published in French), 5 volumes, Moscow 1954 to 1965

The following translations of Lyapunov's main work "A general problem of the stability of movement" (first published in Russian in 1892 and in Charkow in 1902) have so far existed:

  • Liapounoff: Problème general de la stabilité du mouvement , Annales de la faculté des sciences de Toulouse, Sér. 2, 9 (1907), pp. 203-474, numdam
  • General problems of the stability of the movement. Annals of Mathematics Studies ( ISSN  0066-2313 ) No. 17, Princeton 1949 (reprint of 1907 edition)
  • The General Problem of the Stability of Motion. Taylor & Francis 1992, ISBN 978-0-7484-0062-1

Other works are:

  • About constant helical movements of a solid body in a liquid ( О постоянных винтовых движениях твердого тела в жидкости ), 1890
  • Sur la stabilité des figures ellipsoidales d'équilibre d'un liquids animé d'un mouvement de rotation , Annales de la Faculté des sciences de l'Université de Toulouse, 2nd series, volume 6, 1904, pp. 5–116, numdam
  • On a series of linear differential equations in the theory (Sur une série dans la théorie des équations differentielles linéaires etc.) , St. Petersburg 1902
  • Research in the theory of the figure des corps célestes, St. Petersburg, 1903
  • Sur l'équation de Clairaut et les équations plus générales de la théorie de la figure des planetes , St. Petersburg, 1904
  • Sur unprobleméme de Tchebycheff , St. Petersburg, 1905
  • Nouvelle forme du théorème sur la limite de probabilité , Memoirs Acad. Imp. Sci. St. Petersburg 1902, pp. 1–24 (reprinted in William J. Adams (Ed.), The life and times of the central limit theorem, 2nd edition, AMS 2009)
  • Sur une proposition de la theory des probabilités , Bull. Acad. Sci. St. Petersburg, Volume 13, 1906, pp. 126–128 (reprinted in Adams, loc.cit.)
  • Sur les figures d'équilibre peu différentes des ellipsoids d'une masse liquide homogène doulée d'un mouvement de rotation, 4 volumes, St. Petersburg, 1906–1914
  • Problème de minimum dans une question de stabilité des figures d'équilibre d 'masse fiuide en rotation, St. Petersburg, 1908
  • Sur certaines séries de figures d'équilibre d'un liquide hétérogéne en rotation, 2 volumes, Leningrad, 1925, 1927 (published posthumously)
  • Work on potential theory (Russian), Moscow, Leningrad, 1949

See also

literature

  • AT Grigorian: Lyapunov, Aleksandr Mikhailovich . In: Charles Coulston Gillispie (Ed.): Dictionary of Scientific Biography . tape 8 : Jonathan Homer Lane - Pierre Joseph Macquer . Charles Scribner's Sons, New York 1973, p. 559-563 .
  • Joseph P. LaSalle, Solomon Lefschetz : The Stability Theory by Ljapunoff , (Series: BI University Pocket Book ) Bibliographisches Institut, Mannheim 1967
  • Nicolas Rouche et al .: Stability Theory by Lyapunov's Direct Method. Springer, Berlin 1977, ISBN 3-540-90258-9
  • Vangipuram Lakshmikantham et al .: Vector Lyapunov Functions and Stability Analysis of non linear Systems. Kluwer Academic, Dordrecht 1991, ISBN 0-7923-1152-3

Web links

Individual evidence

  1. ^ List of members since 1666: Letter L. Académie des sciences, accessed on January 13, 2020 (French, here the spelling: Alexandre Liapounoff).
  2. ↑ VI Smirnov, AP Youchkevitch (ed.), Correspondance de AM Liapunov avec H. Poincare. Cahiers du séminaire d'histoire des mathématiques, 8 (1987), p. 1-18, numdam ( Memento from August 9, 2016 in the Internet Archive )
personal data
SURNAME Lyapunov, Alexander Michailowitsch
ALTERNATIVE NAMES Ляпунов, Александр Михайлович (Russian)
BRIEF DESCRIPTION Russian mathematician and physicist
DATE OF BIRTH June 6, 1857
PLACE OF BIRTH Yaroslavl
DATE OF DEATH November 3, 1918
Place of death Odessa