Geodesic
Generic distributional chaos and principal measure in linear dynamics
Zongbin Yin1 ; Qigui Yang1
1 Department of Mathematics South China University of Technology Guangzhou, 510640, P.R. China
Annales Polonici Mathematici, Tome 118 (2016) no. 1, pp. 71-94.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Generic distributional chaos and principal measure in linear dynamics are investigated. Sufficient conditions for a $C_0$-semigroup of operators on a Fréchet space to be generically distributionally chaotic are provided and applied to concrete examples. Furthermore, the distributionally chaotic dynamics of product operators (product $C_0$-semigroups, respectively) are considered. It is shown that under certain conditions, the product operator is generically distributionally chaotic if and only if there is a factor operator exhibiting generic distributional chaos. Another interesting finding is that there exist distributionally chaotic (but not hypercyclic) operators whose principal measure could be less than any fixed positive number.
DOI : 10.4064/ap3908-9-2016
Keywords: generic distributional chaos principal measure linear dynamics investigated sufficient conditions semigroup operators chet space generically distributionally chaotic provided applied concrete examples furthermore distributionally chaotic dynamics product operators product semigroups respectively considered shown under certain conditions product operator generically distributionally chaotic only there factor operator exhibiting generic distributional chaos another interesting finding there exist distributionally chaotic hypercyclic operators whose principal measure could fixed positive number

Zongbin Yin 1 ; Qigui Yang 1

1 Department of Mathematics South China University of Technology Guangzhou, 510640, P.R. China 
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Zongbin Yin; Qigui Yang. Generic distributional chaos and principal measure in linear dynamics. Annales Polonici Mathematici, Tome 118 (2016) no. 1, pp. 71-94. doi : 10.4064/ap3908-9-2016. http://geodesic.mathdoc.fr/articles/10.4064/ap3908-9-2016/

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