Lyapunov is a Russian surname that is sometimes also romanized as Ljapunov, Liapunov or Ljapunow. Notable people with the surname include:
Prokopy Lyapunov (d. 1611), Russian statesman
Zakhary Lyapunov (d. after 1612), Russian statesman, Prokopy Lyapunov's brother
Mikhail Lyapunov (1820–1868), Russian astronomer
Aleksandr Lyapunov (1857–1918), son of Mikhail, Russian mathematician and mechanician, after whom the following are named:
Lyapunov dimension
Lyapunov equation
Lyapunov exponent
Lyapunov function
Lyapunov fractal
Lyapunov stability
Lyapunov's central limit theorem
Lyapunov time
Lyapunov vector
Lyapunov (crater)
Sergei Lyapunov (1859–1924), son of Mikhail, Russian composer
Boris Lyapunov (1862–1943), son of Mikhail, Russian expert in Slavic studies
Alexey Lyapunov (1911–1973), Russian mathematician