Pointwise topological stability and persistence

[摘要] We prove that if a homeomorphism of a compact metric space is equicontinuous and pointwise topologically stable, then it is persistent (in the sense of Lewowicz [12]). The proof relies on the notion of persistent measure which has its own interest. We compute the Borel hierarchy of these measures and prove that they are not necessarily topologically stable (in the sense of [9]). (C) 2019 Published by Elsevier Inc.

[发布日期] 2019-12-15

[关键词] Persistent homeomorphisrn;Persistent measure;Topologically stable point