中文摘要：

本文研究了光滑映射芽在RN作用下的轨道切空间的问题.利用乘积积分理论的方法,获得了光滑映射芽关于右等价群的一类子群RN的无限决定性的结果,推广了光滑映射芽是RN-有限决定的结果.

英文摘要：

In this paper, the tangent space to the orbit of smooth map-germs under the action of RN is investigated. By produce integral theory, the infinite determinacy of smooth map-germs relative to a subgroup RN of right equivalent group is obtained, and the necessary and sufficient conditions for a smooth map-germ to be finitely RN-determined are extended.