Whitney umbrella and slow-motion bifurcations of relaxation-type equations
Whitney umbrella and slow-motion bifurcations of relaxation-type equations
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惠特尼伞和松弛型方程的慢动分岔
DOI：
10.1007/s10958-005-0081-7
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发表时间：
2005
影响因子：
--
通讯作者：
A. A. Davydov
中科院分区：
文献类型：
--
作者：
A. A. Davydov
当慢速度不切于折叠临界值集时，在方程折叠的Whitney折叠型奇点附近，得到了含二维慢变量的松弛型方程的一般单参数慢运动族的光滑轨道规范形.例如，参数的类属值的类属族由V.I.发现的方程（dy/dx）2=x（x-y）2或（dy/dx）2= x的原点处的芽来描述。Arnold和M. Cibrario，分别在一个适当的选择后，光滑的局部坐标纤维的参数空间。
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)2or (dy/dx)2=xfound by V. I. Arnold and M. Cibrario, respectively, after an appropriate choice of smooth local coordinates fibered over the parameter spaces.