迭代运算使不连续映射变为光滑映射  

Iteration Changes Discontinuous Mappings Into Smooth Mappings

作　　者：刘晓华[1] 罗天琦[2] LIU Xiao-hua;LUO Tian-qi(School of Mathematics and Physics,Leshan Normal University,Leshan Sichuan 614000,China;School of Teacher Education,Leshan Normal University,Leshan Sichuan 614000,China)

机构地区：[1]乐山师范学院数理学院,四川乐山614000 [2]乐山师范学院教师教育学院,四川乐山614000

出　　处：《西南大学学报（自然科学版）》2021年第8期84-92,共9页Journal of Southwest University(Natural Science Edition)

基　　金：四川省教育厅重点科研基金项目(18ZA0242);乐山师范学院重点项目(LZD014).

摘　　要：很容易找到一些不连续自映射,它们的迭代是光滑的,表明迭代运算可以使不连续映射变为光滑映射.为了研究这种变化和避免复杂计算,本文研究在区间(0,1)上只有一个可去间断点的分段C^(1)自映射的二次迭代的C^(1)光滑性,给出了它们的二次迭代是C^(1)光滑映射的充要条件.It is easy to find some discontinuous self-mappings whose iterates are smooth mappings,suggesting that iteration can change discontinuous mappings into smooth mappings.In order to research this change and avoid complicated computation,in this paper we investigate C^(1)smoothness of the second order iterates of piecewise C^(1)self-mappings on the compact interval(0,1),each of which has only one removable discontinuity.The necessary and sufficient conditions under which the second order iterates are C^(1)smooth mappings are given.

关 键 词：迭代 可去间断点 C^(1)光滑 分段光滑 

分 类 号：O174[理学—数学]