Affiliation:
1. School of Science, Guangdong Ocean University, Zhanjiang 524025, China
Abstract
We prove that if a continuous, Lyapunov stable mapffrom a compact metric spaceXinto itself is topologically transitive and has the asymptotic average shadowing property, thenXis consisting of one point. As an application, we prove that the identity mapiX:X→Xdoes not have the asymptotic average shadowing property, whereXis a compact metric space with at least two points.
Funder
Natural Science Foundation of Guangdong Province
Cited by
14 articles.
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