Distributionally chaotic $C_0$-semigroups on complex sectors
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918107529871360 |
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| author | Jiang, Zhen Li, Jian Yang, Yini |
| author_facet | Jiang, Zhen Li, Jian Yang, Yini |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_00891 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distributionally chaotic $C_0$-semigroups on complex sectors Jiang, Zhen Li, Jian Yang, Yini Functional Analysis Dynamical Systems 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. |
| title | Distributionally chaotic $C_0$-semigroups on complex sectors |
| topic | Functional Analysis Dynamical Systems |
| url | https://arxiv.org/abs/2503.00891 |