We examine smooth four-dimensional vector fields reversible under some smooth involution \(L\) that has a smooth two-dimensional submanifold of fixed points. Our main interest here is in the orbit structure of such a system near two types of heteroclinic connections involving saddle-foci and heteroclinic orbits connecting them. In both cases we found families of symmetric periodic orbits, multi-round heteroclinic connections and countable families of homoclinic orbits of saddle-foci. All this suggests that the orbit structure near such connections is very complicated. A non-variational version of the stationary Swift – Hohenberg equation is considered, as an example, where such structure has been found numerically.

我们检查在具有平滑二维定点子流形的平滑对合\(L\)下可逆的平滑四维向量场。我们在这里主要感兴趣的是这样一个系统的轨道结构，靠近两种类型的异宿连接，包括鞍焦点和连接它们的异宿轨道。在这两种情况下，我们都发现了对称周期轨道族、多轮异宿连接和鞍焦点同宿轨道族。所有这些都表明，此类连接附近的轨道结构非常复杂。作为一个例子，我们考虑了平稳 Swift-Hohenberg 方程的非变分版本，其中这种结构已经在数值上被发现。