度量空间中强链回归点集的研究

On Strong Chain Recurrent Point Set in Metric Space

研究了紧致度量空间中连续自映射强链回归点集的动力学性质,利用映射的一致收敛性,得到了强链回归点的一些结论:同胚映射f的强链回点集等于它的逆映射f-1的强链回归点集;同胚映射f的强链回归点集对f强不变;连续映射f限制在它的强链回归点集上形成的强链回归点集就是连续映射f在度量空间上形成的强链回归点集.最后给出一个例子,表明了强链回归点的概念不同于链回归点的概念.这些结论推广和改进了早期文献中链回归点的相关结果.

The dynamical properties of strong chain recurrent point set of continuous self mapping has been studied in the compact metric spaces. By the uniform convergence of the map, some conclusions of strong chain recurrent points have been obtained: The strong chain recurrent point set of the homeomorphic mapping is equal to strong chain recurrent point set of its inverse mapping;The strong chain recurrent point set of the homeomorphism map is its strong invariant set;The strong chain recurrent point set of the restriction of the continuous map f to SCR (f) is equal to the strong chain recurrent point set of the map f in the compact metric space. Finally, an example is given to show that the concept of strong chain recurrent point is different from the concept of chain recurrent point. Hence, these conclusions generalize and improve the related results of chain recurrent point in the early literature.