We study shadowing properties of continuous actions of the groups ${\mathbb Z}^p$ and ${\mathbb Z}^p\times {\mathbb R}^p$. Necessary and sufficient conditions are given under which a linear action of ${\mathbb Z}^p$ on ${\mathbb C}^m$ has a Lipschitz shadowing property.
Keywords:
study shadowing properties continuous actions groups mathbb mathbb times mathbb necessary sufficient conditions given under which linear action mathbb mathbb has lipschitz shadowing property
Affiliations des auteurs :
Sergei Yu. Pilyugin
1
;
Sergei B. Tikhomirov
1
1
Faculty of Mathematics and Mechanics St. Petersburg State University Bibliotechnaya pl., 2 198904, St. Petersburg, Russia
@article{10_4064_fm179_1_7,
author = {Sergei Yu. Pilyugin and Sergei B. Tikhomirov},
title = {Shadowing in actions of some {Abelian} groups},
journal = {Fundamenta Mathematicae},
pages = {83--96},
year = {2003},
volume = {179},
number = {1},
doi = {10.4064/fm179-1-7},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm179-1-7/}
}
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AU - Sergei Yu. Pilyugin
AU - Sergei B. Tikhomirov
TI - Shadowing in actions of some Abelian groups
JO - Fundamenta Mathematicae
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VL - 179
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Sergei Yu. Pilyugin; Sergei B. Tikhomirov. Shadowing in actions of some Abelian groups. Fundamenta Mathematicae, Tome 179 (2003) no. 1, pp. 83-96. doi: 10.4064/fm179-1-7
