Abstract
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.
Citation
Xiongping Dai. "A note on the shadowing lemma of Liao: A generalized and improved version." Tohoku Math. J. (2) 62 (4) 509 - 526, 2010. https://doi.org/10.2748/tmj/1294170344
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