形式等价与有穷级等价
Formal and finite order equivalences
摘要：
我们证明了$C^{n}$中两个实解析子集的芽族是形式等价的当且仅当它们在任何有穷级上是等价的。我们进一步应用相同的技术，以获得类似的声明，实解析自映射和向量场的共轭下的等价性。另一方面，我们提供了一个例子，两套芽的平滑曲线是等价的任何有穷级，但不正式等价。
英文摘要：
We show that two families of germs of real-analytic subsets in $C^{n}$ are formally equivalent if and only if they are equivalent of any finite order. We further apply the same technique to obtain analogous statements for equivalences of real-analytic self-maps and vector fields under conjugations. On the other hand, we provide an example of two sets of germs of smooth curves that are equivalent of any finite order but not formally equivalent.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
