A Lyapunov function is a scalar function used to study the stability of a dynamical system, providing a way to demonstrate that the system will remain close to an equilibrium point over time. By examining the behavior of this function along trajectories of the system, one can infer the stability characteristics of equilibria without explicitly solving the system's differential equations. This concept is crucial in analyzing dynamical systems, particularly in projective spaces, where understanding stability in relation to geometric structures becomes essential.
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