Abstract The C 1 Hartman Theorem states that every C 1 , 1 contraction in R d admits C 1 linearization. In this paper we prove C 1 , β linearizability for C 1 , α contractive (or expansive) random diffeomorphisms with appropriate constants 0 α 1 and 0 β 1 , which implies a random version of the C 1 Hartman Theorem. Moreover, the conjugacy is proved to be tempered. This result strengthens related results even in the deterministic case, lowering the C 1 , 1 condition to C 1 , α and enhancing the C 1 smoothness of the conjugacy to C 1 , β in R d . In the proof we use a smooth weak-stable invariant manifold in the random sense to construct the conjugacy and to overcome difficulties from nonuniformity and measurability.

中文翻译：

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随机动力系统的 C1 Hartman 定理

摘要 C 1 哈特曼定理指出，R d 中的每个C 1 , 1 收缩都允许C 1 线性化。在本文中，我们证明了 C 1 , β 线性化 C 1 ，α 收缩（或膨胀）随机微分同胚具有适当的常数 0 α 1 和 0 β 1 ，这意味着 C 1 Hartman 定理的随机版本。此外，证明共轭是被缓和的。即使在确定性情况下，该结果也加强了相关结果，将 C 1 , 1 条件降低到 C 1 , α 并增强了 R d 中与 C 1 , β 共轭的 C 1 平滑度。在证明中，我们使用随机意义上的平滑弱稳定不变流形来构造共轭，并克服非均匀性和可测量性带来的困难。