Abstract
A systematic approximation method for time evolutions of distribution functions of deterministic dynamical systems is developed when the distribution functions are not far from Gaussian. For simplicity and definiteness, the procedure of the method is shown by taking a simple dynamical system, that is, one-dimensional autonomous nonlinear oscillator. An essential point of the method is to replace an original initial value problem of the evolution of a distribution function by an appropriate initial value problem of the evolution of a Gaussian distribution function by using the Kullback-Leibler's information. Basic properties of an initial value problem posed by the method are also studied.
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