Yao, Yuwu; Chen, Xiu; Niu, Xin Distributional chaos on complex sectors. (Chinese. English summary) Zbl 1399.37024 Acta Math. Sci., Ser. A, Chin. Ed. 37, No. 5, 950-961 (2017). Summary: We characterize the densely distributional chaos for the translation semigroup, with a sector in the complex plane as index set, defined on a weighted function space. A sufficient condition is given for the translation semigroup to be distributionally chaotic in terms of the integrability of the admissible weight function, and in terms of the upper density of a subset of the index set. In addition, we study the index set and show that the translation semigroup is also distributionally chaotic on some subsets of the index set. MSC: 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 54H20 Topological dynamics (MSC2010) Keywords:Banach space; distributional chaos; translation semigroup; complex sector PDF BibTeX XML Cite \textit{Y. Yao} et al., Acta Math. Sci., Ser. A, Chin. Ed. 37, No. 5, 950--961 (2017; Zbl 1399.37024)