We prove a semi-invertible Oseledets theorem for cocycles acting on measurable fields of Banach spaces, i.e. we only assume invertibility of the base, not of the operator. As an application, we prove an invariant manifold theorem for nonlinear cocycles acting on measurable fields of Banach spaces.

中文翻译：

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Banach空间场上的Oseledets分裂和不变流形

我们证明了作用于Banach空间的可测量域上的同轮摩托车的半可逆Oseledets定理，即，我们仅假设基的可逆性，而不是算符的可逆性。作为一个应用，我们证明了作用于Banach空间的可测量场上的非线性cocycles的不变流形定理。