光滑映射芽关于t-P-K-等价的有限决定性

光滑映射芽关于t-P-K-等价的有限决定性 The Finite Determinacy of Smooth Map Germs Relative to t-P-K-equivalence 许静波 XU Jingbo 1 first-author 陈亮 CHEN Liang 2 孙伟志 SUN Weizhi 3 吉林师范大学数学学院 吉林师范大学数学学院 School of Mathematics,Jilin Normal University School of Mathematics,Jilin Normal University 东北师范大学数学与统计学院 东北师范大学数学与统计学院 School of Mathematics and Statistics,Northeast Normal University School of Mathematics and Statistics,Northeast Normal University 长春理工大学理学院 长春理工大学理学院 School of Science,Changchun University of Science and Technology School of Science,Changchun University of Science and Technology 给出光滑映射芽关于t-P-K-等价与t-S.P-K-等价的有限决定性概念,利用Mather的有限决定性理论,证得光滑映射芽在上述等价关系下的有限决定性定理,为对具有有区别参数的光滑映射芽的分类研究提供了有力工具. The notions of finite determinacy of smooth map germs relative to t-P-K-equivalence and t-S.PK-equivalence are established,and Finite Determinacy Theorem of smooth map germs about the two equivalent relations is shown.The result is a powerful tool of the classification of smooth mapping germs with distinguished parameters relative to the above equivalent relations. 光滑映射芽 t-P-K-等价 t-S.P-K-等价 有限决定性 smooth map germ t-P-K-equivalence t-S.P-K-equivalence finite determinacy 10.14188/j.1671-8836.2013.06.015 O174 国家自然科学基金（10871035,10801027,11301215）;吉林省科技发展计划青年基金（201201081）资助项目;吉林省教育厅“十二五”科学技术研究项目（2013213）;四平市科技局项目（2011004）;吉林师范大学博士启动项目 2013-06-01 2021-04-01 6 59