HOME > Table of Contents and Abstracts > Vol. 62, No. 4
Tohoku Mathematical Journal
SECOND SERIES VOL. 62, NO. 4
|Tohoku Math. J.|
62 (2010), 509-526
A NOTE ON THE SHADOWING LEMMA OF LIAO: A GENERALIZED AND IMPROVED VERSION
(Received August 10, 2009, revised February 9, 2010)
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.
2000 Mathematics Subject Classification.
Primary 37C50; Secondary 37D30.
Key words and phrases.
Shadowing lemma, exponential closing property, quasi-hyperbolicity, local diffeomorphism.
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