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

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.