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Catastrophe theory analyzes degenerate critical points of the potential function — points where not just the first derivative, but one or more higher derivatives of the potential function are also zero. These are called the germs of the catastrophe geometries. The degeneracy of these critical points can be unfolded by expanding the potential function as a Taylor series in small perturbations of the parameters.
Catastrophe theory analyzes degenerate critical points of the potential function — points where not just the first derivative, but one or more higher derivatives of the potential function are also zero. These are called the germs of the catastrophe geometries. The degeneracy of these critical points can be unfolded by expanding the potential function as a Taylor series in small perturbations of the parameters.
突变论分析势函数的退化临界点，在退化临界点处，势函数不仅一阶导数为零，而且有一个或多个高阶导数也为零，这被视为突变几何的萌芽。临界点的退化可以通过在参数的微小扰动中将势函数按照泰勒级数来展开。