A+ CATEGORY SCIENTIFIC UNIT

Generic distributional chaos and principal measure in linear dynamics

Volume 118 / 2016

Zongbin Yin, Qigui Yang Annales Polonici Mathematici 118 (2016), 71-94 MSC: Primary 47A16, 47D06; Secondary 54H20. DOI: 10.4064/ap3908-9-2016 Published online: 24 November 2016

Abstract

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.

Authors

  • Zongbin YinDepartment of Mathematics
    South China University of Technology
    Guangzhou, 510640, P.R. China
    e-mail
  • Qigui YangDepartment of Mathematics
    South China University of Technology
    Guangzhou, 510640, P.R. China
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image