0392926 20240111140831.520130625235959.9 000320059800012 84878928174 10.1142/S0218127413500843 9 s. P cav_un_epca*02567760218-1274235 (2013)World Scientific Publishing Hyperspace chaos shadowing Bernoulli shift cav_un_auth*0101066 Beran Zdeněk Teorie řízení Department of Control Theory TŘ TR UTIA-B Department of Control Theory Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0101074 Čelikovský Sergej Teorie řízení Department of Control Theory TŘ TR UTIA-B Department of Control Theory Ústav teorie informace a automatizace AV ČR, v. v. i. textový dokument http://library.utia.cas.cz/separaty/2013/TR/beran-0392926.pdf 261 kB GA13-20433S GA ČR cav_un_auth*0292613 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. 2014 BC 2 4 A 4a 20231122135642.7 RVO:67985556 http://hdl.handle.net/11104/0221980 MATHEMATICSINTERDISCIPLINARYAPPLICATIONS|MULTIDISCIPLINARYSCIENCES 1.052 0.195 8.III 0.00835 0.359 4328 246 0.670 ScienceCitationIndex Q1 29.949 53.876 Q3 Q2 2013 Soubory v repozitáři: beran-0392926.pdf 84878928174 SCOPUS 000320059800012 WOS textový dokument 261 kB cav_un_epca*0256776 International Journal of Bifurcation and Chaos 0218-1274 1793-6551 Roč. 23 č. 5 2013 , 1350084-1-1350084-9 World Scientific Publishing