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The solutions of the variational equation through the orbits of $\\mathcal{K}$ induce linear skew-product semiflows on the bundles $\\mathcal{K}\\times W^{1,\\infty}([-r,0],\\mathbb{R}^n)$ and $\\mathcal{K}\\times C([-r,0],\\mathbb{R}^n)$. 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The solutions of the variational equation through the orbits of $\\mathcal{K}$ induce linear skew-product semiflows on the bundles $\\mathcal{K}\\times W^{1,\\infty}([-r,0],\\mathbb{R}^n)$ and $\\mathcal{K}\\times C([-r,0],\\mathbb{R}^n)$. 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