三维映射在不动点附近的正规形  

The Normal Form of a 3D Diffeomorphism near the Fixed Point

作　　者：何兰 HE Lan(School of Mathematical Sciences,Chongqing Normal University,Shapingba,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆沙坪坝401331

出　　处：《内江师范学院学报》2018年第12期55-59,共5页Journal of Neijiang Normal University

基　　金：国家自然科学基金项目(11671061);重庆市自然科学基金(cstc2018jcyjAX0418)

摘　　要：对于2维非双曲微分同胚,在幂一情形下运用经典理论可以得到其最简的正规形,而在3维空间中非双曲微分同胚的正规形还不足够简化.为此,在幂一情形下运用线性算子的核空间与补空间等理论,推出3维非双曲微分同胚的更简正规形.For a 2-dimensional non-hyperbolic diffeomorphism,classical theory can be used in the uni-potent case to obtain the simplest normal form.However,the normal form of a 3-dimensional non-hyperbolic diffeomorphism is not simple enough.For this reason,in the uni-potent case theories of the kernel space and complementary space of linear operators are used to derive the simpler normal form of a 3-dimensional non-hyperbolic diffeomorphism.

关 键 词：非双曲微分同胚 正规形 内积 正交补空间 伴随算子 

分 类 号：O193[理学—数学]