| Autor: |
Shengnan He, Xin Liu, Zongbin Yin, Xiaoli Sun |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
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| Zdroj: |
Mathematics, Vol 12, Iss 20, p 3167 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
2227-7390 |
| DOI: |
10.3390/math12203167 |
| Popis: |
In this paper, we investigate the relationships among point transitivity, topological transitivity, Li–Yorke chaos, and the existence of irregular vectors for a linear semiflow {Tt}t∈Δ indexed with a complex sector. We reveal the equivalence between topological transitivity and point transitivity for a linear semiflow {Tt}t∈Δ, especially in case the range of some operator Tt,t∈Δ is not dense. We also prove that Li–Yorke chaos is equivalent to the existence of a semi-irregular vector and that point transitivity is stronger than the existence of an irregular vector for any linear semiflow Ttt∈Δ. At last, unlike the conclusion for traditional linear dynamical systems, we show that there exists a Li–Yorke chaotic C0-semigroup Ttt∈Δ without irregular vectors. The results and proof methods presented in this paper demonstrate the differences in the dynamical behavior between linear semiflows {Tt}t∈Δ and traditional linear systems with the acting semigroup S=Z+ and S=R+. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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