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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/2412.05603 |
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| _version_ | 1866912147817103360 |
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| author | Al-Qaiwani, Rayyan Callaway, Mark Rasmussen, Martin |
| author_facet | Al-Qaiwani, Rayyan Callaway, Mark Rasmussen, Martin |
| contents | We prove that projectivised finite-dimensional linear random dynamical systems possess a unique finest weak Morse decomposition. Based on this result, we define the Morse spectrum and investigate its basic properties. In particular, we show that the Morse spectrum is given by a finite union of closed intervals. Furthermore we demonstrate that under a bounded growth condition, the Morse spectrum coincides with the non-uniform dichotomy spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05603 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Morse spectrum for linear random dynamical systems Al-Qaiwani, Rayyan Callaway, Mark Rasmussen, Martin Dynamical Systems We prove that projectivised finite-dimensional linear random dynamical systems possess a unique finest weak Morse decomposition. Based on this result, we define the Morse spectrum and investigate its basic properties. In particular, we show that the Morse spectrum is given by a finite union of closed intervals. Furthermore we demonstrate that under a bounded growth condition, the Morse spectrum coincides with the non-uniform dichotomy spectrum. |
| title | The Morse spectrum for linear random dynamical systems |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2412.05603 |