orbital shadowing
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2020 ◽  
Vol 269 (2) ◽  
pp. 1360-1382
Author(s):  
Ming Li


2020 ◽  
Vol 12 (1) ◽  
pp. 146-154
Author(s):  
Manseob Lee

AbstractLet f : M → M be a diffeomorphism on a closed smooth n(≥ 2) dimensional manifold M. We show that C1 generically, if a diffeomorphism f has the orbital shadowing property on locally maximal chain transitive sets which admits a dominated splitting then it is hyperbolic.



2019 ◽  
Vol 268 ◽  
pp. 106903 ◽  
Author(s):  
Joel Mitchell
Keyword(s):  


2019 ◽  
Vol 17 (1) ◽  
pp. 191-201 ◽  
Author(s):  
Manseob Lee

Abstract Let M be a closed smooth Riemannian manifold and let f : M → M be a diffeomorphism. We show that if f has the C1 robustly asymptotic orbital shadowing property then it is an Anosov diffeomorphism. Moreover, for a C1 generic diffeomorphism f, if f has the asymptotic orbital shadowing property then it is a transitive Anosov diffeomorphism. In particular, we apply our results to volume-preserving diffeomorphisms.



2017 ◽  
Vol 262 (10) ◽  
pp. 5022-5051 ◽  
Author(s):  
Shaobo Gan ◽  
Ming Li
Keyword(s):  


2016 ◽  
Vol 38 (1) ◽  
pp. 143-154 ◽  
Author(s):  
CHRIS GOOD ◽  
JONATHAN MEDDAUGH

Let $f:X\rightarrow X$ be a continuous map on a compact metric space, let $\unicode[STIX]{x1D714}_{f}$ be the collection of $\unicode[STIX]{x1D714}$-limit sets of $f$ and let $\mathit{ICT}(f)$ be the collection of closed internally chain transitive subsets. Provided that $f$ has shadowing, it is known that the closure of $\unicode[STIX]{x1D714}_{f}$ in the Hausdorff metric coincides with $\mathit{ICT}(f)$. In this paper, we prove that $\unicode[STIX]{x1D714}_{f}=\mathit{ICT}(f)$ if and only if $f$ satisfies Pilyugin’s notion of orbital limit shadowing. We also characterize those maps for which $\overline{\unicode[STIX]{x1D714}_{f}}=\mathit{ICT}(f)$ in terms of a variation of orbital shadowing.



2016 ◽  
Vol 53 (2) ◽  
pp. 581-588
Author(s):  
Mohammad Reza Bagherzad Sessary ◽  
Keonhee Lee






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