Tohoku Mathematical Journal

A note on the shadowing lemma of Liao: A generalized and improved version

Xiongping Dai

Full-text: Open access

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.

Article information

Source
Tohoku Math. J. (2), Volume 62, Number 4 (2010), 509-526.

Dates
First available in Project Euclid: 4 January 2011

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1294170344

Digital Object Identifier
doi:10.2748/tmj/1294170344

Mathematical Reviews number (MathSciNet)
MR2768757

Zentralblatt MATH identifier
1225.37030

Subjects
Primary: 37C50: Approximate trajectories (pseudotrajectories, shadowing, etc.)
Secondary: 37D30: Partially hyperbolic systems and dominated splittings

Keywords
Shadowing lemma exponential closing property quasi-hyperbolicity local diffeomorphism

Citation

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


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