The well-known Hartman-Grobman Theorem says that a C¹ hyperbolic diffeomorphism F can be locally linearized by a homeomorphism Φ. For parameterized systems F_θ, known results show that the corresponding homeomorphisms Φ_θ exist uniquely in a functional space equipped with the supremum norm and depend continuously on the parameter θ. In this paper, we further extend the results to Hölder dependence of Φ_θ on θ by Pugh’s strategy, but introducing a kind of special Hölder norm instead of the usual supremum norm in the proof to control the linear parts of F_θ. This requires a new Hölder linearization result for every F_θ.

中文翻译：

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参数化Hartman-Grobman定理的Hölder依赖

著名的Hartman-Grobman定理说，C ¹双曲微分同构F可以通过同胚同构Φ局部线性化。对于参数化系统˚F _θ，已知结果表明相应的同胚Φ _θ在配备有确界范数的功能空间唯一地存在，所述参数连续地取决于θ。在本文中，我们进一步延伸的结果，Φ持有依赖性_θ上θ由Pugh的策略，但是在验算引入一种特殊的支架规范，而不是通常确界范数来控制的线性部分˚F _θ。这需要每一个新的持有者，线性化结果˚F _θ。