In the scalar case, the nondegeneracy of heteroclinic orbits is a well-known property, commonly used in problems involving nonlinear elliptic, parabolic or hyperbolic P.D.E. On the other hand, Schatzman proved that in the vector case this assumption is generic, in the sense that for any potential $W:{\mathbb{R}}^m\to \mathbb{R}$, $m\ge 2$, there exists an arbitrary small perturbation of $W$, such that for the new potential minimal heteroclinic orbits are nondegenerate. However, to the best of our knowledge, nontrivial explicit examples of such potentials are not available. In this paper, we prove the nondegeneracy of heteroclinic orbits for potentials $W:{\mathbb{R}}^2\to [0,\infty )$ that can be written as $W\left(z\right)={\left|f\left(z\right)\right|}^2$, with $f:ℂ\to ℂ$ a holomorphic function.

在标量情况下，异宿轨道的非简并性是众所周知的性质，常用于涉及非线性椭圆、抛物线或双曲 PDE 的问题。对于任何潜在 $宽：{\mathbb{电阻}}^{米}\to \mathbb{电阻}$, $米\ge 2$，存在任意的小扰动 $宽$，使得新的潜在最小异宿轨道是非简并的。然而，据我们所知，这种势的非平凡的明确例子是不可用的。在本文中，我们证明了势能的异宿轨道的非简并性$宽：{\mathbb{电阻}}^2\to [0,\infty )$ 可以写成 $宽\left(z\right)={\left|F\left(z\right)\right|}^2$， 和 $F：ℂ\to ℂ$ 一个全纯函数。