We give characterizations of the hyperbolicity of a nonautonomous one-sided dynamics defined by a sequence of linear operators, in terms of the hyperbolicity of an associated evolution map defined on a Banach space of sequences. We consider a large family of spaces of sequences besides $$L^p$$ L p spaces. Moreover, we discuss the general cases when the dynamics may be invertible only along the unstable direction and of a general nonuniform exponential behavior of the dynamics given by a sequence of norms instead of a single norm.

中文翻译：

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通过进化图的单边双曲线

我们根据在 Banach 序列空间上定义的相关进化图的双曲性，给出了由一系列线性算子定义的非自治单边动力学的双曲性特征。除了 $$L^p$$L p 空间之外，我们还考虑了一大类序列空间。此外，我们讨论了动力学可能仅沿不稳定方向可逆的一般情况，以及由一系列范数而不是单个范数给出的动力学的一般非均匀指数行为。