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