For a linear nonautonomous dynamics, we give a characterization of its hyperbolicity in terms of a certain cocycle, both for discrete and continuous time. The base of the cocycle is obtained taking the closure of the translations of the dynamics with respect to the topology of uniform convergence on compact sets, which in the case of discrete time corresponds to pointwise convergence.

中文翻译：

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双曲线的等价概念

对于线性非自治动力学，我们根据离散和连续时间的特定共循环给出其双曲性的表征。Cocycle 的基是通过关于紧集上一致收敛拓扑的动力学平移的闭包获得的，在离散时间的情况下，这对应于逐点收敛。