迭代下保持不变的自映射

Self-Mappings of Remaining Unchanged under Iteration

通过对自映射的迭代研究可以提供系统在未来一串离散时刻的状态变化趋势.自映射的迭代作为某一决定性系统变化过程的时间离散取样是离散动力系统研究的重点.在迭代下能保持不变的自映射反映了系统在时间离散取样时未来的状态和现在完全一致.研究了什么自映射在迭代下能保持不变的,得到了有这类自映射的充分必要条件.

The research of iteration of self-mappings can provide the changing tendency of discrete time state system in the future.Meanwhile,the iteration of self-mappings can be seen as a discrete sampling of time in the changing procedure of a decisive system,which constitutes the core content of study in the discrete dynamical system.Self-mappings of remaining unchanged under the iteration reflect the system to be completely consistent between now and future under the discrete sampling of time.This paper studies what kinds of self-mappings can be remaining unchanged under iteration,and obtains the sufficient and necessary condition having these selfmappings.