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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.10764 |
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| _version_ | 1866913270211805184 |
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| author | Backes, Lucas Dragicevic, Davor Pituk, Mihaly |
| author_facet | Backes, Lucas Dragicevic, Davor Pituk, Mihaly |
| contents | It is known that hyperbolic non\-autonomous linear delay differential equations in a finite dimensional space are Hyers--Ulam stable and hence shadowable. The converse result is available only in the special case of autonomous and periodic linear delay differential equations with a simple spectrum. In this paper, we prove the converse and hence the equivalence of all three notions in the title for a general class of nonautonomous linear delay differential equations with uniformly bounded coefficients. The importance of the boundedness assumption is shown by an example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10764 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Shadowing, Hyers--Ulam stability and hyperbolicity for nonautonomous linear delay differential equations Backes, Lucas Dragicevic, Davor Pituk, Mihaly Dynamical Systems It is known that hyperbolic non\-autonomous linear delay differential equations in a finite dimensional space are Hyers--Ulam stable and hence shadowable. The converse result is available only in the special case of autonomous and periodic linear delay differential equations with a simple spectrum. In this paper, we prove the converse and hence the equivalence of all three notions in the title for a general class of nonautonomous linear delay differential equations with uniformly bounded coefficients. The importance of the boundedness assumption is shown by an example. |
| title | Shadowing, Hyers--Ulam stability and hyperbolicity for nonautonomous linear delay differential equations |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2401.10764 |