AI 中文总结
本文研究离散动力系统中各类敏感性的关系，引入半强β-n-敏感性等新敏感性形式，证明强多传递性蕴含强多敏感性，明确β-n-敏感性在迭代下的保持性，相关结果改进并推广了已有结论。
AI 中文摘要
本文研究离散动力系统中β-n-敏感性与其他形式敏感性之间的关系，给出成为（强）β-n-敏感性的若干不同充分条件（等价条件），这些结果改进并推广了已有成果。此外，引入并研究关于α的半强β-n-敏感性与（强）多β-n-敏感性，证明强多传递性蕴含强多敏感性，进一步改进已有结论。最后，得到（半）强β-n-敏感性在迭代下保持，但β-n-敏感性不保持的结论。
英文摘要
In this paper, we investigate the relationships between the $β$-$n$-sensitivity and other forms of sensitivity in discrete dynamical systems. And we present some different sufficient conditions (equivalent condition) to be (strongly) $β$-$n$-sensitive. These results improve and extend some existing ones. Moreover, we introduce and study the semi-strong $β$-$n$-sensitivity and (strong) multi-$β$-$n$-sensitivity with respect to $α$. Besides, we proved that strongly multi-transitivity implies strongly multi-sensitivity, which improves some existing ones. Finally, we obtain that (semi-)strongly $β$-$n$-sensitivity is preserved under iterations but $β$-$n$-sensitivity fails.
