Article
| Title: | Characterization of shadowing for linear autonomous delay differential equations (English) |
| Author: | Pituk, Mihály |
| Author: | Stavroulakis, John Ioannis |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 1 |
| Year: | 2025 |
| Pages: | 289-296 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | A well-known shadowing theorem for ordinary differential equations is generalized to delay differential equations. It is shown that a linear autonomous delay differential equation is shadowable if and only if its characteristic equation has no root on the imaginary axis. The proof is based on the decomposition theory of linear delay differential equations. (English) |
| Keyword: | delay differential equation |
| Keyword: | linear autonomous equation |
| Keyword: | shadowing |
| MSC: | 34K06 |
| MSC: | 34K27 |
| MSC: | 37D99 |
| DOI: | 10.21136/CMJ.2024.0191-23 |
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| Date available: | 2025-03-11T16:03:42Z |
| Last updated: | 2025-03-19 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152909 |
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| Reference: | [1] Backes, L., Dragičević, D.: Shadowing for infinite dimensional dynamics and exponential trichotomies.Proc. R. Soc. Edinb., Sect. A, Math. 151 (2021), 863-884. Zbl 1470.37028, MR 4259329, 10.1017/prm.2020.42 |
| Reference: | [2] Backes, L., Dragičević, D., Pituk, M., Singh, L.: Weighted shadowing for delay differential equations.Arch. Math. 119 (2022), 539-552. Zbl 1515.34064, MR 4496984, 10.1007/s00013-022-01769-3 |
| Reference: | [3] Brzdęk, J., Popa, D., Raşa, I., Xu, B.: Ulam Stability of Operators.Mathematical Analysis and its Applications. Academic Press, London (2018). Zbl 1393.39001, MR 3753562, 10.1016/c2015-0-06292-x |
| Reference: | [4] Buse, C., Saierli, O., Tabassum, A.: Spectral characterizations for Hyers-Ulam stability.Electron. J. Qual. Theory Differ. Equ. 2014 (2014), Article ID 30, 14 pages. Zbl 1324.34022, MR 3218777, 10.14232/ejqtde.2014.1.30 |
| Reference: | [5] Hale, J. K., Lunel, S. M. Verduyn: Introduction to Functional Differential Equations.Applied Mathematical Sciences 99. Springer, New York (1993). Zbl 0787.34002, MR 1243878, 10.1007/978-1-4612-4342-7 |
| Reference: | [6] Palmer, K.: Shadowing in Dynamical Systems: Theory and Applications.Mathematics and its Applications (Dordrecht) 501. Kluwer, Dordrecht (2000). Zbl 0997.37001, MR 1885537, 10.1007/978-1-4757-3210-8 |
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