AI 中文总结
研究非自治动力系统的近端关系和最大等度连续因子，考虑由一致收敛映射序列生成的系统和周期系统，通过集体收敛等得出相关结论，确定最大等度连续因子的核，给出周期系统近端性准则，还证明了假设的必要性。
AI 中文摘要
本文研究紧致度量空间上非自治动力系统的近端型关系和最大等度连续因子。考虑了两类系统：由一致收敛映射序列生成的系统和周期系统。对于一致收敛生成元，集体收敛和一致刚性意味着非自治系统的区域近端关系等于极限自治系统的区域近端关系，且若极限系统是等度连续的，非自治系统的近端关系等于自治极限系统的近端关系。在相同设定下，最大等度连续因子的核被确定为包含相应自治系统的自治等度连续结构关系且由所有生成元保持的最小闭等价关系。对于周期系统，区域近端性和巴拿赫近端性由周期映射确定，给出了一个关于平均等度连续性和平均敏感性关系的准则。例子表明这些结果中使用的假设是必要的。
英文摘要
This paper studies proximal-type relations and maximal equicontinuous factors for non-autonomous dynamical systems on compact metric spaces. Two classes of systems are considered: systems generated by uniformly convergent sequences of maps and periodic systems. For uniformly convergent generators, collective convergence and uniform rigidity imply that the regional proximal relation for the non-autonomous system is equal to the regional proximal relation for the limit autonomous system and if the limit system is equicontinuous, then the proximality relation for the non-autonomous system is equal to the proximal relation for the autonomous limit system. In the same setting, the kernel of the maximal equicontinuous factor is identified as the smallest closed equivalence relation containing the autonomous equicontinuous structure relation of the corresponding autonomous system and preserved by all generators. For periodic systems, regional proximality and Banach proximality are determined by the period map, yielding a criterion in terms of mean equicontinuity and the relation of sensitivity in the mean. Examples show that the hypotheses used in these results are necessary.
Comments24 pages
