We prove that, if \(f:X\rightarrow X\) is a regular curve homeomorphism then the set of periodic points is either empty or dense in the set of non-wandering points. Moreover, we prove that each infinite minimal set is approximated by periodic orbits and is conjugate to an adding machine when the set of periodic points is not empty. Furthermore, we give a characterization of equicontinuous regular curve homeomorphisms

中文翻译：

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正则曲线同胚的周期点

我们证明，如果\（f：X \ rightarrow X \）是规则曲线同胚，则周期点集在非漂移点集中要么为空，要么为密。此外，我们证明了当周期点集不为空时，每个无限极小集都由周期轨道近似并且与加法器共轭。此外，我们给出了等连续正则曲线同胚的特征