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Universal perturbations of linear differential equations

Authors:	Gerd Herzog

Institution:	Mathematisches Institut I, Universität Karlsruhe, D-76128 Karlsruhe, Germany

Abstract:	Let $X:0,\infty)\to L(\mathbb{R} ^n)$ be a fundamental solution of with and $X^{-1}$ bounded on $0,\infty)$ . We prove that there exist arbitrary small matrix functions $B:0,\infty)\to L(\mathbb{R} ^n)$ with limit as $t\to \infty$ such that has solutions with $y(0,\infty))$ dense in $\mathbb{R} ^n$ .

Keywords:	Linear differential equations dense orbits universal elements

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