Ma, Xin; Han, Yinghao; Zhang, Guangda Strong shadowing property on a weak form hyperbolic set. (Chinese. English summary) Zbl 1199.37042 J. Shenyang Norm. Univ., Nat. Sci. 26, No. 1, 17-19 (2008). Summary: In this paper, we give a kind of \(C^1\) map on a weak form hyperbolic set, i.e. Steinlein-hyperbolic set, via the notion of strong shadowing, we obtain a generalized shadowing lemma. Let \(H\) be a Banach space, \(\phi: V\rightarrow H\) a \(C^1\) map on an open subset \(V\) of \(H\), then the \(C^1\) map of \(\phi\) has the strong shadowing property on \(T\). Assuming that \(T\subset V\) is a Steinlein-hyperbolic set of \(\phi\). MSC: 37D05 Dynamical systems with hyperbolic orbits and sets 37C75 Stability theory for smooth dynamical systems Keywords:Banach space; \(C^1\) map; hyperbolic set; strong shadowing property PDFBibTeX XMLCite \textit{X. Ma} et al., J. Shenyang Norm. Univ., Nat. Sci. 26, No. 1, 17--19 (2008; Zbl 1199.37042)