In 1876 Lyapunov entered the Physico-Mathematical faculty of the University of Saint Petersburg, but after one month he transferred to the Mathematics department of the university.

Lyapunov returned to Saint Petersburg in 1902, after being elected acting member of the Academy of Science as well as ordinary professor in the Faculty of Applied Mathematics of the university.

However, at the urging of his maternal uncle, the physicist Lyapunov, Zaitsev was allowed to enroll at Kazan ' university to study economics.

In 1880 Lyapunov received a gold medal for a work on hydrostatics.

After Chebysheve became a professor of mathematics in Moscow himself, his two most illustrious gradute students were Andrei Andreyevich Markov ( the elder ) and Alexandr Lyapunov.

When the measure μ is associated to a mass distribution on a sufficiently smooth hypersurface S ( a Lyapunov surface of Hölder class C < sup > 1, α </ sup >) that divides R < sup > d </ sup > into two regions D < sub >+</ sub > and D < sub >−</ sub >, then the Newtonian potential of μ is referred to as a simple layer potential.

Estimates in 1993 put the Lyapunov time horizon for predictability at around 50 years, after which the uncertainty region becomes larger with each close approach to a planet.

Without the perturbations from the terrestrial planets the Lyapunov time would be close to 10, 000 years.

The exponent is named after Aleksandr Lyapunov.

Named after the Russian mathematician Aleksandr Mikhailovich Lyapunov, Lyapunov functions are important to stability theory and control theory.

Lyapunov stability is named after Aleksandr Lyapunov, a Russian mathematician who published his book " The General Problem of Stability of Motion " in 1892.

This and related equations are named after the Russian mathematician Aleksandr Lyapunov.

It is named after the Russian mathematician Aleksandr Lyapunov who died in 1918.

His doctoral students included some of the most famous Soviet mathematicians: Pavel Aleksandrov, Nina Bari, Aleksandr Khinchin, Andrey Kolmogorov, Alexander Kronrod, Mikhail Lavrentyev, Alexey Lyapunov, Lazar Lyusternik, Pyotr Novikov, Lev Schnirelmann and Pavel Urysohn.

Lyapunov would maintain a scientific contact with Markov during all his life.

Among his well-known students were the prolific mathematicians Dmitry Grave, Aleksandr Korkin, Aleksandr Lyapunov, and Andrei Markov.

The same mathematics is sometimes used to show that relative entropy is a Lyapunov function of a Markov process in detailed balance, and other chemistry contexts.

Scholars like Rudolf E. Kalman and Aleksandr Lyapunov are well-known among the people who have shaped modern control theory.

At his uncle's family, Lyapunov studied with his distant cousin Natalia Rafailovna, who became his wife in 1886.

Prokopy Petrovich Lyapunov () ( died 1611 ) was a Russian statesman of Rurikid stock, who helped deliver Moscow from Polish interventionists.

But what Lyapunov taught us was new to me and I had never seen this material in any textbook.

In January 1611, Zarutsky joined the First People's Volunteer Army, which had been fighting with the Polish invaders in Moscow under the command of Prokopy Lyapunov.

:* Escape-time fractals – use a formula or recurrence relation at each point in a space ( such as the complex plane ); usually quasi-self-similar ; also known as " orbit " fractals ; e. g., the Mandelbrot set, Julia set, Burning Ship fractal, Nova fractal and Lyapunov fractal.

These eigenvalues are also called local Lyapunov exponents.

It can also calculate the conditional Lyapunov exponents for coupled identical systems.

The same underlying mathematics, however, was also discovered independently several times: by George William Hill ( 1877 ), Gaston Floquet ( 1883 ), and Alexander Lyapunov ( 1892 ).

Lyapunov stability methods have also been applied to finding equilibrium solutions in traffic assignment problems.

In 1887, he graduated from the Kharkov University, where he was a student of Aleksandr Lyapunov.

In 1863, M. V. Lyapunov retired from his scientific career and relocated his family to his wife's estate at Bolobonov, in the Simbirsk province ( now Ulyanovsk Oblast ).

The next year Lyapunov became a full professor at Kharkiv University.

In 1895 Lyapunov became privatdozent and was proposed to accept the chair of mechanics at Kharkiv University, where he went the same year.

About the initial stay at Kharkiv, Lyapunov writes in his autobiography:

In 1930 O. Perron constructed an example of the second-order system, the first approximation of which has negative Lyapunov exponents along a zero solution of the original system but, at the same time, this zero solution of original nonlinear system is Lyapunov unstable.

Also it is possible to construct reverse example when first approximation has positive Lyapunov exponents along a zero solution of the original system but, at the same time, this zero solution of original nonlinear system

Informally, a Lyapunov function is a function that takes positive values everywhere except at the equilibrium in question, and decreases ( or is non-increasing ) along every trajectory of the ODE.

Working at the Crimean Astrophysical Observatory since 1978, she has discovered a number of asteroids, including the Amor asteroid 5324 Lyapunov and the Trojan asteroid 3063 Makhaon.

A complexor is generated by a set of deterministic nonlinear equations that has at least one positive Lyapunov exponent.

* Alexander Lyapunov ( 1857 – 1918 ) in the 1890s marks the beginning of stability theory.

The stability of a general dynamical system with no input can be described with Lyapunov stability criteria.

Stability for nonlinear systems that take an input is input-to-state stability ( ISS ), which combines Lyapunov stability and a notion similar to BIBO stability.

To address these questions several notions of stability have been introduced in the study of dynamical systems, such as Lyapunov stability or structural stability.

Notable Russian scientists include Dmitri Mendeleev, Nikolay Bogolyubov, Andrei Kolmogorov, Ivan Pavlov, Nikolai Semyonov, Dmitri Ivanenko, Nikolai Lobachevsky, Alexander Lodygin, Alexander Popov ( one of inventors of radio ), Nikolai Zhukovsky, Alexander Prokhorov and Nikolay Basov ( co-inventors of laser ), Georgiy Gamov, Vladimir Zworykin, Lev Pontryagin, Sergei Sobolev, Pavel Yablochkov, Aleksandr Butlerov, Andrei Sakharov, Dmitry Ivanovsky, Sergey Korolyov and Mstislav Keldysh ( creators of the Soviet space program ), Aleksandr Lyapunov, Mikhail Dolivo-Dobrovolsky, Andrei Tupolev, Yuri Denisyuk ( the first practicable method of holography ), Mikhail Lomonosov, Vladimir Vernadsky, Pyotr Kapitsa, Igor Sikorsky, Ludvig Faddeev, Zhores Alferov, Konstantin Novoselov, Fyodor Shcherbatskoy, Nikolai Trubetzkoy etc.

Aleksandr Mikhailovich Lyapunov (, ; – November 3, 1918 ) was a Russian mathematician, mechanician and physicist.

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.

Lyapunov was born in Yaroslavl, Russian Empire.

His father Mikhail Vasilyevich Lyapunov ( 1820 – 1868 ) was an astronomer and a head of the Demidovski lyceum.

His brother, Sergei Lyapunov, was a gifted composer and pianist.

After the death of his father in 1868, Aleksandr Lyapunov was educated by his uncle R. M. Sechenov, brother of the physiologist Ivan Mikhailovich Sechenov.

Lyapunov wrote his first independent scientific works under the guidance of the professor of mechanics, D. K. Bobylev.