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@article{30274,
author = {Mlíchová, Michaela and Štefánková, Marta},
article_location = {Abingdon},
article_number = {5},
doi = {http://dx.doi.org/10.1080/10236198.2017.1309035},
keywords = {generic chaos; dense chaos; induced map; hyperspaces; Li-Yorke chaos},
language = {eng},
issn = {1023-6198},
journal = {Journal of Difference Equations and Applications},
title = {On generic and dense chaos for maps induced on hyperspaces},
url = {https://www.tandfonline.com/doi/full/10.1080/10236198.2017.1309035},
volume = {24},
year = {2018}
}
TY - JOUR
ID - 30274
AU - Mlíchová, Michaela - Štefánková, Marta
PY - 2018
TI - On generic and dense chaos for maps induced on hyperspaces
JF - Journal of Difference Equations and Applications
VL - 24
IS - 5
SP - 685-700
EP - 685-700
PB - Taylor and Francis Ltd.
SN - 10236198
KW - generic chaos
KW - dense chaos
KW - induced map
KW - hyperspaces
KW - Li-Yorke chaos
UR - https://www.tandfonline.com/doi/full/10.1080/10236198.2017.1309035
L2 - https://www.tandfonline.com/doi/full/10.1080/10236198.2017.1309035
N2 - A continuous map f on a compact metric space X induces in a natural way the map f’ on the hyperspace K(X) of all closed non-empty subsets of X. We study the question of transmission of chaos between f and f’. We deal with generic, generic e-, dense and dense e-chaos for interval maps. We prove that all four types of chaos transmit from f to f, while the converse transmission from f to f’ is true for generic, generic e-and dense e-chaos. Moreover, the transmission of dense eand generic e-chaos from f’ to f is true for maps on general compact metric spaces.
ER -
MLÍCHOVÁ, Michaela and Marta ŠTEFÁNKOVÁ. On generic and dense chaos for maps induced on hyperspaces. \textit{Journal of Difference Equations and Applications}. Abingdon: Taylor and Francis Ltd., 2018, vol.~24, No~5, p.~685-700. ISSN~1023-6198. Available from: https://dx.doi.org/10.1080/10236198.2017.1309035.
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