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arXiv · 2503.00891

Distributionally chaotic $C_0$-semigroups on complex sectors

Zhen Jiang·Jian Li·Yini Yang
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Abstract

We explore distributional chaos for $C_0$-semigroups of linear operators on Banach spaces whose index set is a sector in the complex plane. We establish the relationship between distributional sensitivity and distributional chaos by characterizing them in terms of distributionally (semi-)irregular vectors. Additionally, we provide conditions under which a $C_0$-semigroup admits a linear manifold of distributionally irregular vectors. Furthermore, we delve into the study of distributional chaos for the translation $C_0$-semigroup on weighted $L_p$-spaces with a complex sector as the index set. We obtain a sufficient condition for dense distributional chaos, expressed in terms of the weight. In particular, we construct an example of a translation $C_0$-semigroup with a complex sector index set that is Devaney chaotic but not distributionally chaotic.

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Zhen Jiang, Jian Li, Yini Yang. 2025-03-02. Distributionally chaotic $C_0$-semigroups on complex sectors. https://doi.org/10.1007/s43037-025-00446-1

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