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Unexpected Behavior of Nonautonomous Linear Dynamical Systems in Two Dimensions

Authors:	Email author" target="_blank">N?V?Krylov Email author

Institution:	(1) University of Minnesota, 127 Vincent Hall, Minneapolis, 55455, MN, USA

Abstract:	We show two examples of systems $\dot{z}_{t} = -na_{t} z_{t}$ in $\mathbb{R}^{2}$ with $a_{t} = a_{t}^{*} \geqslant 0$ such that \|Z_t\| is strictly decreasing in time for any n but $\|z_{t}\| \nrightarrow 0$ as $n \rightarrow \infty$ .

Keywords:	Non autonomous systems linear ODEs
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