$C^{1}$ Smoothness of the Conjugacy in a Delayed Nonautonomous Hartman--Grobman Theorem via $μ$-Dichotomies
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| Format: | Preprint |
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2025
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| _version_ | 1866911114839719936 |
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| author | Castañeda, Álvaro Elorreaga, Heli |
| author_facet | Castañeda, Álvaro Elorreaga, Heli |
| contents | We investigate the differentiability of the conjugacy in a nonautonomous version of the Hartman--Grobman Theorem for systems with finite delay, where the linear part satisfies a $μ$-dichotomy. Under suitable conditions on the nonlinear perturbation, the conjugacy is shown to be a $C^{1}$ diffeomorphism. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_15696 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $C^{1}$ Smoothness of the Conjugacy in a Delayed Nonautonomous Hartman--Grobman Theorem via $μ$-Dichotomies Castañeda, Álvaro Elorreaga, Heli Dynamical Systems Classical Analysis and ODEs 34D09, 34k27, 34k20, 34k06 We investigate the differentiability of the conjugacy in a nonautonomous version of the Hartman--Grobman Theorem for systems with finite delay, where the linear part satisfies a $μ$-dichotomy. Under suitable conditions on the nonlinear perturbation, the conjugacy is shown to be a $C^{1}$ diffeomorphism. |
| title | $C^{1}$ Smoothness of the Conjugacy in a Delayed Nonautonomous Hartman--Grobman Theorem via $μ$-Dichotomies |
| topic | Dynamical Systems Classical Analysis and ODEs 34D09, 34k27, 34k20, 34k06 |
| url | https://arxiv.org/abs/2508.15696 |