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Bibliography

Journal Article

Chaos on hyperspace

Beran Zdeněk, Čelikovský Sergej

: International Journal of Bifurcation and Chaos vol.23, 5 (2013)

: GA13-20433S, GA ČR

: Hyperspace, chaos, shadowing, Bernoulli shift

: 10.1142/S0218127413500843

: http://library.utia.cas.cz/separaty/2013/TR/beran-0392926.pdf

(eng): In this paper, the chaotic behavior of a set-valued mapping F : X → 2X, where X is a compact space, is investigated. The existence of the generalized shadowing property in the hyperspace 2X is proved. Based on the generalized shadowing property of the set-valued mappings F and the assumption of the existence of an unstable chain recurrent point of the mapping F, it is shown that the Bernoulli system of bi-directional shifts is embedded in the sense of semiconjugacy into the image of mapping F, i.e. Smale’s chaos in the set-valued system F is thereby proved.

: BC

2019-01-07 08:39