Lyapunov spectra behavior for linear discrete-time systems under small perturbations
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866916926089854976 |
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| author | Czornik, Adam Makarov, Evgenii Niezabitowski, Michal Popova, Svetlana Zaitsev, Vasilii |
| author_facet | Czornik, Adam Makarov, Evgenii Niezabitowski, Michal Popova, Svetlana Zaitsev, Vasilii |
| contents | We investigate the behavior of the Lyapunov spectrum of a linear discrete-time system under the action of small perturbations in order to obtain some verifiable conditions for stability and openness of the Lyapunov spectrum. To this end we introduce the concepts of broken away solutions and splitted systems. The main results obtained are a necessary condition for stability and a sufficient condition for the openness of the Lyapunov spectrum, which is given in terms of the system itself. Finally, examples of using the obtained results are presented. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2106_14691 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Lyapunov spectra behavior for linear discrete-time systems under small perturbations Czornik, Adam Makarov, Evgenii Niezabitowski, Michal Popova, Svetlana Zaitsev, Vasilii Dynamical Systems 39A06, 39A22, 39A30 We investigate the behavior of the Lyapunov spectrum of a linear discrete-time system under the action of small perturbations in order to obtain some verifiable conditions for stability and openness of the Lyapunov spectrum. To this end we introduce the concepts of broken away solutions and splitted systems. The main results obtained are a necessary condition for stability and a sufficient condition for the openness of the Lyapunov spectrum, which is given in terms of the system itself. Finally, examples of using the obtained results are presented. |
| title | Lyapunov spectra behavior for linear discrete-time systems under small perturbations |
| topic | Dynamical Systems 39A06, 39A22, 39A30 |
| url | https://arxiv.org/abs/2106.14691 |