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2008 International Workshop on Dynamical System and Realted Topics
(2008 / vol.10 / no.2)
Diffeomorphisms with Limit Shadowing property
Taeyoung Choi
Pages. 111-119   



In this article, we give a characterization of two-sided limit shadowing property for homeomorphism of $S^1$.
Under $C^1$-robust point of view, we consider hyperbolicity of invariant closed subset of smooth manifold such as chain recurrent set
and chain component via various limit shadowing properties and show some results for them.



1. Limit Shadowing Property
2. TSLmSP and $sl$-TSLmSP of invariant sets
3. TSLmSP on the circle maps
4. $C^1$-non density of $sl$-TSLmSP
5. Stable $sl$-TSLmSP on closed manifold
6. Stable $sl$-TSLmSP on the chain component



Limit shadowing property, two-sided limit shadowing property, hyperbolicity, stable TSLmSP, chain recurrent set, homoclinic class, chain component



37D30, 37D20,37C29