摘要

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 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.