Lyapunov's Stability Theorem is a fundamental result in the field of dynamical systems that provides criteria for determining the stability of an equilibrium point. It establishes conditions under which small perturbations in the system will not lead to significant deviations from the equilibrium, thereby allowing for predictions about the system's long-term behavior. The theorem is crucial in understanding how systems respond to changes and is closely related to Lyapunov exponents, which quantify the rates of separation of infinitesimally close trajectories in various dynamical systems.
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