复扇形指标集上的分布混沌

Distributional Chaos on Complex Sectors

该文刻画了具有扇形指标集的转移半群在权函数空间中上的稠密分布混沌.由相容权函数的可积性,以及指标集子集的上稠性,对转移半群的分布混沌性给出了一个充分条件.此外,该文还对指标集进行了讨论,给出了转移半群在指标集的某些子集上也是分布混沌的.

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 suificient condition is given for the translation semigroup to be distributionally chaotic in terms of the 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.