Lyapunov is a Russian surname that is sometimes romanized as Ljapunov, Liapunov or Ljapunow. Notable people with the surname include:
Prokopy Lyapunov (? –1611), Russian statesmanZakhary Lyapunov (? – after 1612), Russian statesman, Prokopy Lyapunov's brotherMikhail Lyapunov (1820–1868), Russian astronomerAleksandr Lyapunov (1857–1918), Russian mathematician and mechanicianLyapunov equationLyapunov exponentLyapunov functionLyapunov fractalLyapunov stabilityLyapunov's central limit theoremLyapunov vectorLyapunov (crater)Sergei Lyapunov (1859–1924), Russian composerBoris Lyapunov (1862–1943), Russian expert in Slavic studiesAlexey Lyapunov (1911–1973), Russian mathematician