On generic and dense chaos for maps induced on hyperspaces

@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 a 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, roč.~24, č.~5, s.~685-700. ISSN~1023-6198. Dostupné z: https://dx.doi.org/10.1080/10236198.2017.1309035.