Abstract
A generalized critical point is characterized by the vanishing of certain linear relationships. In particular, the dynamics near such a point are non-linear. In this paper, we study fluctuations at such points of spatially homogeneous systems. We discuss thermodynamic critical points as a special case; but the main emphasis is on stochastic kinetic equations. We show that fluctuations at a critical point cannot be characterized by a Gaussian density, but more complicated densities can be used. The theory is applied to the critical harmonic oscillator.
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