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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/2401.10767 |
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| _version_ | 1866916513564327936 |
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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 linear delay difference equations are shadowable on the half-line. In this paper, we prove the converse and hence the equivalence between hyperbolicity and the positive shadowing property for the following two classes of linear delay difference equations: (a)~for nonautonomous equations with finite delays and uniformly bounded compact coefficient operators in (possibly infinite-dimensional) Banach spaces, (b)~for Volterra difference equations with infinite delay in finite dimensional spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10767 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Shadowing and hyperbolicity for linear delay difference equations Backes, Lucas Dragicevic, Davor Pituk, Mihaly Dynamical Systems It is known that hyperbolic linear delay difference equations are shadowable on the half-line. In this paper, we prove the converse and hence the equivalence between hyperbolicity and the positive shadowing property for the following two classes of linear delay difference equations: (a)~for nonautonomous equations with finite delays and uniformly bounded compact coefficient operators in (possibly infinite-dimensional) Banach spaces, (b)~for Volterra difference equations with infinite delay in finite dimensional spaces. |
| title | Shadowing and hyperbolicity for linear delay difference equations |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2401.10767 |