一类映射在双曲不动点附近的光滑共轭等价正规形

Smoothly Conjugating Normal Forms of Some Maps Near Their Hyperbolic Fixed Points

摘要: 考虑有限维线性空间中的一类局部微分同胚在双曲不动点O附近的光滑共轭等价问题.通过使用正规形方法证明了若局部微分同胚F(x)的Q-射式中的p次多项式映射代表满足UR条件,则在双曲不动点O附近光滑共轭等价于映射DF(O)x,也就是说,DF(O)x是在双曲不动点处的光滑正规形.

Abstract: In this paper,we discuss smoothly conjugating equivalence of some local diffeomorphisms with hy- perbolic fixed points on finite dimensional space.We prove that,under UR condition of polynomial map in Q-jet J^Q(F),DF(O)x is the smooth normal form of F(x) near its hyperbolic fixed point.