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
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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.Abstract:
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.
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