度量G-空间中G-链回归点的G-链等价集

G-chain Equivalent Set of G-chain Recurrent Point in the Metric G-space

根据链回归点和链等价点的定义,给出了G-链回归点和G-链等价点的概念,并研究了度量G-空间中G-链回归点集和G-链等价集的动力学性质,得到如下结果:(1)映射f的G-链回点集等于映射f^n的G-链回归点集;(2)点x关于映射f^n的G-链等价集等于点f^n(x)关于映射f^n的G-链等价集;(3)点x关于映射f的G-链等价集等于集合■;(4)集合CE_G(f^i(x),f^n)在映射f作用下的象等于点f^(i+1)(x)关于映射f^n的G-链等价集.所得结果丰富了度量G-空间中G-链回归点集和G-链等价集的理论.

The concepts of G-chain recurrent point and G-chain equivalent point were derived according to the definition of chain recurrent point and chain equivalent point.In addition,we studied the dynamical properties of G-chain recurrent point set and G-chain equivalent set in the metric G-space and obtained the following result:(1)The G-chain recurrent point set of the mapping f is equal to G-chain recurrent point set of the mapping f n;(2)The G-chain equivalent set of the point x with respect to the mapping f n is equal to the G-chain equivalent set of the point f n(x)with respect to the mapping f n;(3)The G-chain equivalent set of the point x with respect to the mapping f is equal to the set∪n-1 i=0 C E G(f i(x),f n);(4)The image of the set C E G(f i(x),f n)under the mapping f is equal to the G-chain equivalent set of the point f i+1(x)with respect to the mapping f n.These conclusions enrich the theory of G-chain recurrent point set and G-chain equivalent set in the metric G-space.