标题： 关于具有影子性质系统的完全不规则集 显示英文标题

标题： On the completely irregular set for systems with the shadowing property

摘要： 我们证明，对于每一个非唯一遍历的、满足跟踪性质的、作用于没有孤立点的紧致度量空间上的遍历连续映射，完全不规则集是Baire稠密的。 我们还表明，在上述假设下，任何完全不规则点的轨道都是稠密的。 随后，我们分析了遍历性与跟踪性质之间的联系，得出它们在扩张同胚族中的共同作用的一些结果，并讨论几个例子以测试我们结果的适用范围。 显示英文摘要

摘要： We prove that the completely irregular set is Baire generic for every non-uniquely ergodic transitive continuous map which satisfies the shadowing property and acts on a compact metric space without isolated points. We also show that, under the previous assumptions, the orbit of any completely irregular point is dense. Afterwards, we analyze the connection between transitivity and the shadowing property, draw a few consequences of their joint action within the family of expansive homeomorphisms, and discuss several examples to test the scope of our results.