This note is concerned with the effect of small [Formula: see text] perturbations on a discrete dynamical system [Formula: see text], which has heteroclinic repellers. The question to be addressed is whether such perturbed system [Formula: see text] has heteroclinic repellers. It will be shown that if [Formula: see text] is small enough, [Formula: see text] has heteroclinic repellers, which implies that it is chaotic in the sense of Devaney. In addition, if [Formula: see text] and [Formula: see text] has regular nondegenerate heteroclinic repellers, then [Formula: see text] has regular nondegenerate heteroclinic repellers, where [Formula: see text] is a small Lipschitz perturbation of [Formula: see text]. Three examples are presented to validate the theoretical conclusions.

中文翻译：

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具有异宿排斥器的地图的结构稳定性

本说明关注小[公式：参见文本] 扰动对离散动力系统 [公式：参见文本] 的影响，该系统具有异宿排斥。要解决的问题是这种扰动系统[公式：见正文]是否具有异宿排斥。将证明，如果[公式：见正文]足够小，则[公式：见正文]具有异宿排斥，这意味着它在 Devaney 意义上是混沌的。另外，如果[公式：见文]和[公式：见文]有正则非简并异宿排斥，则[公式：见文]有正则非简并异宿排斥，其中[公式：见文]是[公式：见文]的小Lipschitz扰动[公式：见正文]。给出了三个例子来验证理论结论。