Abstract
Smooth orbital normal forms of generic one-parametric families of slow motion of relaxation-type equations with two-dimensional slow variable are obtained near a singular point of the type Whitney-fold of the equation folding when the slow velocity is not tangent to the set of critical values of the folding. For example, a generic family for a generic value of the parameter is described by the germ at the origin of either the equations (dy/dx)2 = x(x - y)2 or (dy/dx)2 = x found by V. I. Arnold and M. Cibrario, respectively, after an appropriate choice of smooth local coordinates fibered over the parameter spaces.
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