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).

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

Among the Saint Petersburg mathematics professors were Chebyshev and his students Aleksandr Nikolaevich Korkin and Yegor Ivanovich Zolotarev.

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

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 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.

In 1908, the Kharkov edition was translated to French and republished by the University of Toulouse: 'Probleme General de la Stabilite du Mouvement, Par M.A.

In 1885, Lyapunov became privatdozent and was proposed to accept the chair of mechanics at Kharkov University, where he went the same year.

"[1] 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.

Not having any teaching obligations, this allowed Lyapunov to focus on his studies and in particular he was able to bring to a conclusion the work on the problem of Chebyshev with which he started his scientific career.

His main preoccupations were the stability of equilibria and the motion of mechanical systems, especially rotating fluid masses, 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.

[1] Like many mathematicians, Lyapunov preferred to work alone and communicated mainly with few colleagues and close relatives.