We use evolution maps to construct center-stable, center-unstable and center invariant manifolds with optimal regularity for a nonautonomous dynamics with discrete time. The proofs comprise essentially two steps: first we reformulate the original problem in terms of an autonomous problem involving evolutions maps, and then we apply an autonomous result to construct autonomous invariant manifolds that we are able to push back to the original problem. We also describe how the invariant manifolds vary with the perturbations. The main novelty of our work is the method of proof, which leads to simple proofs.

中文翻译：

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进化图和中心流形

对于具有离散时间的非自治动力学，我们使用演化图来构造具有最佳规则性的中心稳定，中心不稳定和中心不变流形。证明基本上包括两个步骤：首先，我们根据涉及进化图的自治问题来重新表述原始问题，然后我们将自治结果应用于构造能够推回到原始问题的自治不变流形。我们还描述了不变流形如何随扰动而变化。我们工作的主要新颖之处在于证明方法，这导致了简单的证明。