Abstract
We study the asymptotic diagonalization of a system consisting of an \(L_{{\text{loc}}}^p \)-matrix plus a finite number of \(L^{m_i } \)-perturbations on an interval I 0=[t 0, ∞), where p, m i∈[1, ∞). Using linear skew-product flows and spectral theory, we show that if the unperturbed system has full spectrum over its omega-limit set, then the entire system is asymptotically diagonalizable almost everywhere.
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Bodine, S.I., Sacker, R.J. A New Approach to Asymptotic Diagonalization of Linear Differential Systems. Journal of Dynamics and Differential Equations 12, 229–245 (2000). https://doi.org/10.1023/A:1009054904419
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DOI: https://doi.org/10.1023/A:1009054904419