AI 中文总结
本文研究向量丛上Hartman-Grobman定理的Hölder正则性，构造等价连续丛范数与合适截断函数，完成相关正则性论证。
AI 中文摘要
本文研究向量丛上Hartman-Grobman定理的Hölder正则性，同时考虑沿纤维方向和基方向的正则性。虽主要论证遵循标准方法，但额外工作用于构造与原范数等价的连续丛范数，使线性部分在首次迭代处成为双曲型。对定理的局部版本，还需在向量丛上构造合适的截断函数，该工作通过单位分解实现。
英文摘要
In this paper, we study Holder regularity of the Hartman-Grobman theorem on vector bundles, considering regularity both along the fiber direction and along the base direction. While the main argument follows standard approaches, additional effort is devoted to constructing a continuous bundle norm that is equivalent to the original norm and with respect to which the linear part becomes hyperbolic at the first iterate. For the local version of the theorem, we further need to construct a suitable cut-off function on the vector bundle, which is achieved by employing partition of unity.
