Tohoku Mathematical Journal
- Tohoku Math. J. (2)
- Volume 62, Number 4 (2010), 509-526.
A note on the shadowing lemma of Liao: A generalized and improved version
The shadowing lemma of Shantao Liao asserts that a “recurrent” quasi-hyperbolic string of a $C^1$-class diffeomorphism of a closed manifold might be closed up by a periodic orbit. In this note, we further show that the string can be closed exponentially up by the periodic orbit. Moreover, this statement also holds for a $C^1$-class map which is only locally diffeomorphic.
Tohoku Math. J. (2), Volume 62, Number 4 (2010), 509-526.
First available in Project Euclid: 4 January 2011
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Dai, Xiongping. A note on the shadowing lemma of Liao: A generalized and improved version. Tohoku Math. J. (2) 62 (2010), no. 4, 509--526. doi:10.2748/tmj/1294170344. https://projecteuclid.org/euclid.tmj/1294170344