Lyapunov theorem may refer to:

• Lyapunov theory, a theorem related to the stability of solutions of differential equations near a point of equilibrium
• Lyapunov central limit theorem, variant of the central limit theorem
• Lyapunov vector-measure theorem, theorem in measure theory that the range of any real-valued, non-atomic vector measure is compact and convex
• Lyapunov–Malkin theorem, a mathematical theorem detailing nonlinear stability of systems

See also

• Aleksandr Lyapunov (1857-1918), Russian mathematician, mechanician and physicist
• Lyapunov equation, used in many branches of control theory, such as stability analysis and optimal control
• Lyapunov fractal, bifurcational fractals derived from an extension of the logistic map in which the degree of the growth of the population periodically switches between two values
• Lyapunov time, characteristic timescale on which a dynamical system is chaotic
• Probability theory, the branch of mathematics concerned with probability
• Dirichlet problem, the problem of finding a function which solves a specified partial differential equation in the interior of a given region that takes prescribed values on the boundary of the region

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