Dynamical systems with the asymptotic average shadowing property. (Chinese. English summary) Zbl 1150.54037

Niu, Yingxuan

Appl. Math., Ser. A (Chin. Ed.) 22, No. 4, 462-468 (2007).

Summary: For a continuous map \(f\) from a compact metric space to itself, it is shown that (1) \(f\) has the asymptotic shadowing property, AASP for short, if and only if the same holds for the shift map on its inverse limit space; (2) if \(f\) has the AASP and is equicontinuous, then \(f\) is a minimal homeomorphism. Further, invariance of the AASP under topological conjugation is investigated.

MSC:

54H20	Topological dynamics (MSC2010)
37B99	Topological dynamics

Keywords:

pseudo orbit tracing property; inverse limit space; minimal homeomorphism