强一致收敛条件下序列系统与极限系统的关系

首先,证明了如果序列系统具有初值敏感性且敏感常数的下极限为正数,则在强一致收敛下,极限系统也具有初值敏感性,并举例说明序列系统中的初值敏感性不能被极限系统所保持,从而得出序列系统中的Auslander-Yorke混沌不具有保持性;其次,还讨论了在强一致收敛的条件下,序列映射周期点(几乎周期点)的上极限包含于极限映射周期点(几乎周期点),并举例说明序列映射周期点(几乎周期点)的上极限不等于极限映射周期点(几乎周期点).

Discussion on the Relation between Sequence System and Limit System under Strongly Uniform Convergence

This paper firstly proves that if the sequence system has sensitive dependence on initial conditions and if sensitive constant of inferior limit is a positive number, then the limit system has sensitive dependence on initial conditions under strongly uniform convergence, gives an example to show that if the sequence system has sensitive dependence on initial conditions, then the sensitive dependence on initial conditions can not be kept by limit system under strongly uniform convergence, thus, derives that Auslander-Yorke chaos in sequence system does not have maintainability, secondly discusses that under strongly uniform convergence, sequence mapping of periodic point or almost periodic point of upper limit is contained in the limit mapping of periodic point or almost periodic point, and gives an example to show that sequence mapping of periodic point or almost periodic point of upper limit is not equal to the limit mapping of periodic point or almost periodic point.