Aleksandr Lyapunov facts for kids

Quick facts for kids Aleksandr Mikhailovich Lyapunov
Born	(1857-06-06)6 June 1857 Yaroslavl, Russian Empire
Died	3 November 1918(1918-11-03) (aged 61) Odessa, Ukrainian People's Republic
Nationality	Russian
Alma mater	Saint Petersburg State University
Known for	Lyapunov function Lyapunov stability Lyapunov exponent Lyapunov central limit theorem Lyapunov vector
Scientific career
Fields	Applied mathematics
Institutions	Saint Petersburg State University Russian Academy of Sciences Kharkov University
Thesis	The general problem of the stability of motion (1892)
Doctoral advisor	Pafnuty Chebyshev
Doctoral students	Vladimir Steklov

Aleksandr Mikhailovich Lyapunov (Russian: Алекса́ндр Миха́йлович Ляпуно́в; 6 June 1857 – 3 November 1918) was a famous Russian mathematician, mechanician (someone who studies how things move), and physicist. His name is sometimes spelled Ljapunov, Liapunov, or Liapounoff. He was the son of astronomer Mikhail Lyapunov and the brother of composer Sergei Lyapunov.

Lyapunov is best known for his work on the stability theory. This theory helps us understand if a system will stay balanced or if it will change over time. He also made many important contributions to mathematical physics and probability theory.

Biography

Early Life and Family

Aleksandr Lyapunov was born in Yaroslavl, Russian Empire. His father, Mikhail Vasilyevich Lyapunov, was an astronomer. Aleksandr's brother, Sergei Lyapunov, became a talented composer and pianist.

In 1863, Aleksandr's father retired. The family moved to his wife's estate in Bolobonov. After his father passed away in 1868, Aleksandr was taught by his uncle, R. M. Sechenov. He studied with his distant cousin, Natalia Rafailovna, who later became his wife in 1886. In 1870, his mother moved with her sons to Nizhny Novgorod. Aleksandr started gymnasium (a type of school) there and graduated with high honors in 1876.

University Education

In 1876, Lyapunov began studying at the University of Saint Petersburg. He first joined the Physico-Mathematical department. However, after just one month, he switched to the Mathematics department.

At the university, he learned from famous professors like Pafnuty Chebyshev. Lyapunov's first independent scientific projects were guided by Professor D. K. Bobylev. In 1880, Lyapunov won a gold medal for his work on hydrostatics (the study of fluids at rest). This work led to his first published scientific papers. He finished his university studies in 1880. He kept in touch with another famous mathematician, Andrey Markov, throughout his life.

Teaching and Research

A big part of Lyapunov's research was about how a spinning fluid mass stays stable. This idea has links to astronomy. Professor Chebyshev suggested this topic for Lyapunov's master's thesis. In 1884, he submitted his thesis titled On the stability of ellipsoidal forms of rotating fluids.

In 1885, Lyapunov became a lecturer and was asked to teach mechanics at Kharkov University. He moved there the same year. At first, he spent a lot of time preparing lessons for his students.

One of his students, Vladimir Steklov, remembered Lyapunov's first lecture. He said Lyapunov was a young man who spoke with a shaky voice. But what Lyapunov taught was new and exciting. Students quickly gained great respect for him.

Lyapunov's most important work was published in 1892. It was a book called The general problem of the stability of motion. This book became his doctoral thesis. He defended it at Moscow University in 1892. In 1908, this important book was translated into French.

Later Years and Legacy

Lyapunov returned to Saint Petersburg in 1902. He was chosen to be a member of the Academy of Science. He also became a professor at the university. This position was open because his former teacher, Chebyshev, had passed away. With fewer teaching duties, Lyapunov could focus more on his research. He finished his work on Chebyshev's problem, which he had started early in his career.

In 1908, he went to the Fourth International Congress of Mathematicians in Rome. He also helped publish the works of another famous mathematician, Euler.

Death

In June 1917, Lyapunov traveled to Odessa with his wife. His wife was very ill with tuberculosis. She passed away on October 31, 1918. Lyapunov died three days later. At that time, he was losing his eyesight due to cataracts.

His Work

Aleksandr Lyapunov in 1908

Lyapunov worked in many areas of mathematics. These included differential equations, potential theory, dynamical systems, and probability theory. He was very interested in how mechanical systems stay stable, especially spinning fluids. He also studied how particles move under gravity.

In mathematical physics, he worked on a problem called the boundary value problem of the Laplace's equation. In potential theory, his 1897 work helped explain important parts of the theory. He also developed many useful ways to find approximate solutions to problems.

In 1899, he created methods to figure out if systems of differential equations are stable. He also developed the modern theory of how a dynamical system stays stable. In probability theory, he built on the work of Chebyshev and Markov. He proved the Central Limit Theorem under more general conditions. The method he used for this proof is now widely used in probability theory.

Lyapunov preferred to work alone. He mostly talked with a few close friends and family. He often worked late into the night. He had many students and was an honorary member of many universities and academies.

Lyapunov's work was very important. Many mathematical ideas are named after him, including:

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

Selected Publications

• 1884, On the stability of ellipsoidal figures of equilibrium of a rotating fluid (in Russian)
• 1892, The general problem of the stability of motion (in Russian)
• 1897, On certain questions connected with Dirichlet's problem (in French)
• 1901, New form of the theorem on the limit of probability (in French)
• 1901, On a theorem of probability theory (in French)

See also