This paper is a summary of results that prove the abundance of one-dimensional strange attractors near a Shil’nikov configuration, as well as the presence of these configurations in generic unfoldings of singularities in \(\mathbb{R}^{3}\) of minimal codimension. Finding these singularities in families of vector fields is analytically possible and thus provides a tractable criterion for the existence of chaotic dynamics. Alternative scenarios for the possible abundance of two-dimensional attractors in higher dimension are also presented. The role of Shil’nikov configuration is now played by a certain type of generalised tangency which should occur for families of vector fields \(X_{\mu}\) unfolding generically some low codimension singularity in \(\mathbb{R}^{n}\) with \(n\geqslant 4\).

本文总结了结果，证明 Shil'nikov 配置附近存在大量一维奇怪吸引子，以及这些配置在 \(\mathbb{R}^{3}\ 中奇点的一般展开中的存在）的最小余维数。在矢量场族中找到这些奇点在分析上是可能的，从而为混沌动力学的存在提供了一个易于处理的标准。还提出了高维二维吸引子可能丰富的替代方案。Shil'nikov 配置的作用现在由某种类型的广义切线发挥，该切线应该发生在矢量场族\(X_{\mu}\)中，一般展开\(\mathbb{R}^{ 中的一些低余维奇点) n}\) 与\(n\geqslant 4\)。