Given a nonempty compact metric space $X$ and a continuous function $f:X \to X$, we study shadowing and $h$-shadowing for the induced maps on hyperspaces, particularly in symmetric products, $F_{n}(X)$, and the hyperspace $2^{X}$ of compact subsets of $X$. We prove that $f$ has shadowing [$h$-shadowing] if and only if $2^{f}$ has shadowing [$h$-shadowing].
Keywords:
given nonempty compact metric space continuous function study shadowing h shadowing induced maps hyperspaces particularly symmetric products hyperspace compact subsets prove has shadowing h shadowing only has shadowing h shadowing
Affiliations des auteurs :
Leobardo Fernández
1
;
Chris Good
1
1
School of Mathematics University of Birmingham Birmingham, United Kingdom B15 2TT
@article{10_4064_fm136_2_2016,
author = {Leobardo Fern\'andez and Chris Good},
title = {Shadowing for induced maps of hyperspaces},
journal = {Fundamenta Mathematicae},
pages = {277--286},
year = {2016},
volume = {235},
number = {3},
doi = {10.4064/fm136-2-2016},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm136-2-2016/}
}
TY - JOUR
AU - Leobardo Fernández
AU - Chris Good
TI - Shadowing for induced maps of hyperspaces
JO - Fundamenta Mathematicae
PY - 2016
SP - 277
EP - 286
VL - 235
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4064/fm136-2-2016/
DO - 10.4064/fm136-2-2016
LA - en
ID - 10_4064_fm136_2_2016
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%A Leobardo Fernández
%A Chris Good
%T Shadowing for induced maps of hyperspaces
%J Fundamenta Mathematicae
%D 2016
%P 277-286
%V 235
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4064/fm136-2-2016/
%R 10.4064/fm136-2-2016
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%F 10_4064_fm136_2_2016
Leobardo Fernández; Chris Good. Shadowing for induced maps of hyperspaces. Fundamenta Mathematicae, Tome 235 (2016) no. 3, pp. 277-286. doi: 10.4064/fm136-2-2016
