Abstract: It is proved that a homeomorphism on a compact metric space with the average-shadowing property has only one chain component which is the whole space. In particular, every point is chain recurrent. Using this result it is given a short proof for a recent theorem of Sakai.

Key words: average-shadowing property, chain component, chain recurrent set, Anosov Diffeomorphism

摘要： 证明了紧致度量空间上具有平均伪轨跟踪性质的同胚只有一个链分支，这个链分支就是全空间。特别的，每个点是链回归的。利用这个结果，给出Sakai新近一个定理的简短证明。

关键词: 平均伪轨跟踪性质, 链分支, 链回归集, Anosov微分同胚