[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c210394

ON STRONG EXPONENTIAL LIMIT SHADOWING PROPERTY

Darabi, Ali (Department of Mathematics Shahid Chamran University of Ahvaz)

Publication Information

Communications of the Korean Mathematical Society / v.37, no.4, 2022 , pp. 1249-1258 More about this Journal

Abstract

In this study, we show that the strong exponential limit shadowing property (SELmSP, for short), which has been recently introduced, exists on a neighborhood of a hyperbolic set of a diffeomorphism. We also prove that Ω-stable diffeomorphisms and 𝓛-hyperbolic homeomorphisms have this type of shadowing property. By giving examples, it is shown that this type of shadowing is different from the other shadowings, and the chain transitivity and chain mixing are not necessary for it. Furthermore, we extend this type of shadowing property to positively expansive maps with the shadowing property.

Keywords

Exponential limit shadowing; limit shadowing; hyperbolic set; ${\Omega}$ -stability; positively expansive map;

Citations & Related Records

Reference

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