Spectrum invariance dilemma for nonuniformly kinematically similar systems
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929215800082432 |
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| author | Gallegos, Claudio A. Jara, Néstor |
| author_facet | Gallegos, Claudio A. Jara, Néstor |
| contents | We unveil instances where nonautonomous linear systems manifest distinct nonuniform $μ$-dichotomy spectra despite admitting nonuniform $(μ, \varepsilon)$-kinematic similarity. Exploring the theoretical foundations of this lack of invariance, we discern the pivotal influence of the parameters involved in the property of nonuniform $μ$-dichotomy such as in the notion of nonuniform $(μ, \varepsilon)$-kinematic similarity. To effectively comprehend these dynamics, we introduce the stable and unstable optimal ratio maps, along with the $\varepsilon$-neighborhood of the nonuniform $μ$-dichotomy spectrum. These concepts provide a framework for understanding scenarios governed by the noninvariance of the nonuniform $μ$-dichotomy spectrum. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_10398 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectrum invariance dilemma for nonuniformly kinematically similar systems Gallegos, Claudio A. Jara, Néstor Chaotic Dynamics Classical Analysis and ODEs 37D25, 34C41, 37C60 We unveil instances where nonautonomous linear systems manifest distinct nonuniform $μ$-dichotomy spectra despite admitting nonuniform $(μ, \varepsilon)$-kinematic similarity. Exploring the theoretical foundations of this lack of invariance, we discern the pivotal influence of the parameters involved in the property of nonuniform $μ$-dichotomy such as in the notion of nonuniform $(μ, \varepsilon)$-kinematic similarity. To effectively comprehend these dynamics, we introduce the stable and unstable optimal ratio maps, along with the $\varepsilon$-neighborhood of the nonuniform $μ$-dichotomy spectrum. These concepts provide a framework for understanding scenarios governed by the noninvariance of the nonuniform $μ$-dichotomy spectrum. |
| title | Spectrum invariance dilemma for nonuniformly kinematically similar systems |
| topic | Chaotic Dynamics Classical Analysis and ODEs 37D25, 34C41, 37C60 |
| url | https://arxiv.org/abs/2401.10398 |