Abstract.
The aim of this paper is to give necessary and sufficient conditions for pointwise and uniform exponential dichotomy of linear skew-product flows. We shall obtain that the pointwise exponential dichotomy of a linear skew-product flow is equivalent to the pointwise admissibility of the pair \((C_0 ({\mathbf{R}},X),C_0 ({\mathbf{R}},X)).\) As a consequence, we prove that a linear skew-product flow π on \(E = X \times \Theta \) is uniformly exponentially dichotomic if and only if the pair \((C_0 ({\mathbf{R}},X),C_0 ({\mathbf{R}},X))\) is uniformly admissible for π.
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Megan, M., Sasu, A.L. & Sasu, B. Perron Conditions for Pointwise and Global Exponential Dichotomy of Linear Skew-Product Flows. Integr. equ. oper. theory 50, 489–504 (2004). https://doi.org/10.1007/s00020-003-1234-z
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DOI: https://doi.org/10.1007/s00020-003-1234-z