强一致收敛条件下拟弱几乎周期性和序列跟踪性的研究

The Research of Quasi-weak Almost Periodic Property and Sequence Shadowing Property Under Strongly Uniform Convergence

在强一致收敛条件下研究了序列映射与极限映射之间关于拟弱几乎周期性和序列跟踪性的动力学性质.利用强一致收敛和等度连续的性质,得到如下结果:(i)设序列映射{f_n}强一致收敛于等度连续映射f,且点列{x_k}是每个映射f_n的拟弱几乎周期点,若■,则x是f的拟弱几乎周期点;(ii)若序列映射{f_n}强一致收敛于等度连续映射f,则■;(iii)设序列映射{f_n}强一致收敛于f,若f_n具有fine序列跟踪性,则f具有序列跟踪性.这些结果丰富了强一致收敛条件下拟弱几乎周期性和序列跟踪性的理论.

The dynamical property of the quasi-weak almost periodic property and sequence shadowing property between the sequence map and the limit map under strongly uniform convergence have been studied in this paper.With the properties of the strong uniform convergence and equicontinuity,we get the following results:(i)Let the sequence map{f_n}converges strongly uniformly to the equicontinuous map f and the sequence of points{x_k}be the quasi-weak almost periodic point of every map f_n.If■,then the point x is the quasi-weak almost periodic point of the map f;(ii)If the sequence map{f_n}converges strongly uniformly to the equicontinuous map f,then■;(iii)Let the sequence map{f_n}converges strongly uniformly to the map f.If f_n has the fine sequence shadowing property,then f has sequence shadowing property.These results enrich the theory of the quasi-weak almost periodic property and sequence shadowing property under strong uniform convergence.