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.
Publié le : 2010-05-15
Classification:
Shadowing lemma,
exponential closing property,
quasi-hyperbolicity,
local diffeomorphism,
37C50,
37D30
@article{1294170344,
author = {Dai, Xiongping},
title = {A note on the shadowing lemma of Liao: A generalized and improved version},
journal = {Tohoku Math. J. (2)},
volume = {62},
number = {1},
year = {2010},
pages = { 509-526},
language = {en},
url = {http://dml.mathdoc.fr/item/1294170344}
}
Dai, Xiongping. A note on the shadowing lemma of Liao: A generalized and improved version. Tohoku Math. J. (2), Tome 62 (2010) no. 1, pp. 509-526. http://gdmltest.u-ga.fr/item/1294170344/