带有周期点圆周自同胚的光滑共轭问题  

Smooth Conjugate Problem of Circle Endomorphisms With Periodic Points

作　　者：楚鹏 CHU Peng(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《内江师范学院学报》2021年第12期37-44,共8页Journal of Neijiang Normal University

基　　金：国家自然科学基金项目(11671061)。

摘　　要：探究圆周上带有周期点的保向自同胚f和g之间的共轭问题,即解决共轭方程φ°f=g°φ.通过对周期点集的分析以及使用逐段定义法,证明了共轭方程存在全局Holder连续解,并且若提高f和g的光滑度,则该解在非周期点集上还是满足C^(r)的.Investigation of the conjugate problem between homeomorphic f and g with periodic points on a circle,is to solve the conjugate equationφ°f=g°φ.By analyzing the periodic point set and using the piecewise definition method,it is proved that the conjugate equation has a global Holder continuous solution,and if the smoothness of f and g is improved,the solution satisfies C^(r) on the non-periodic point set.

关 键 词：C^(r)共轭 周期点 C^(r)微分同胚 HOLDER连续 

分 类 号：O193[理学—数学]