具有渐近平均跟踪性质的参数化IFS
Parameterized IFS with the asymptotic average shadowing property
摘要：
本文将渐近平均跟踪性的概念推广到参数化IFS，并证明了有关定理。特别地，证明了每一个一致收缩IFS都具有渐近平均跟踪性。作为一个重要结果，我们证明了如果紧度量空间X上的连续满射IFS F具有渐近平均跟踪性，则F是链传递的。此外，我们还引入了一些例子，研究了IFS的原渐近平均跟踪性与渐近平均跟踪性之间的关系。例如，有一个IFS F使得具有渐近平均跟踪性质，但不满足跟踪性质。
英文摘要：
In this paper we generalize the notion of asymptotic average shadowing property to parameterized IFS and prove some related theorems on this notion. Specially, this is proved that every uniformly contracting IFS has the asymptotic average shadowing property. As an important result, we show that if a continuous surjective IFS F on a compact metric space X has the asymptotic average shadowing property then F is chain transitive. Moreover, we introduce some examples and investigate the relationship between the original asymptotic average shadowing property and asymptotic average shadowing property for IFS. For example, there is an IFS F such that has the asymptotic average shadowing property but does not satisfy the shadowing property.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
