Given a linear non autonomous dynamical system in two dimensions $x_{n+1}=A_{n}x_{n}$ started at $x_0\neq0$, $A_n\longrightarrow A$ invertible, assume it has zero Lyapunov exponent for all $x_0$, i.e. $\lim_{n\longrightarrow\infty}\log\Vert x_n \Vert/n=0$. Is this enough to conclude that the system is not convergent when started at any of these $x_0$?
2026-03-27 10:30:08.1774607408
Zero Lyapunov exponent
101 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in DYNAMICAL-SYSTEMS
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