Dynamical Systems Of A Class Of N-dimensional Self-Mapping: Point Sets And Periodic Orbits

In this paper, we studied two questions in topological dynamics. First, in 1988, Xiong Jincheng determined point sets of continuous self-mapping f on a closed interval I in <>. Considering 0is descendible mapping, using character of descendible mapping and Cartesian product, one-dimensional self-mapping is extended to n -dimensional self-mapping.In part two, the stability of periodic orbits of self-mapping on a closed, bounded interval was proved by L. Block in 1981. It means that, for any continuous self-mapping f on a closed interval I with a periodic orbit of period p , there is neighborhood U of f in C ( I , I ), such that for every g∈U and every position integer q on the right of p in the Sharkovskii ordering, g has a periodic orbit of period q . In this paper, the stability of periodic orbits on a descendible n -dimensional self-mapping is obtained.