结合可逆代换的迹映射的若干刻划

结合可逆代换的迹映射的若干刻划 Some Description of the Trace Map Associated with Invertible Substitution 刘爱平 LIU Ai-ping 1 2 first-author 文志雄 WEN Zhi-xiong 1 2 武汉大学基础与应用数学基地 武汉大学基础与应用数学基地 Laboratory of Pure and Applied Mathematics, Wuhan University Laboratory of Pure and Applied Mathematics, Wuhan University 武汉大学基础与应用数学基地,湖北,武汉,430072 武汉大学基础与应用数学基地,湖北,武汉,430072 研究迹映射的几个性质 :保测度 ,可积 ,可反 .证明了当一R3 上的映射是迹映射时 ,与其拓扑等价的R2 上的映射是保测度映射 .利用对合矩阵的性质 ,导出了一迹映射是可反映射的一个条件 ,还讨论了迹映射的两个对合之间的关系 . Some properties of trace map are studied, such as exemple measure-preserving, integrable and reversible. When a map on R3 is a trace map associated with invertible substitution, we prove that the map on R2（topollogical equel to the map on R3） is a measure-preserving map. Via studying the involution matric, we can determine a trace map is a reversibe map with substiution matric, at the same time, we can obtain a involution of this trace map. In the end, we study the relationship to the two involutions of a reversible map. 代换 迹映射 保测 可积 可反 substitution trace map measure-preserving integrable reversible O189.1 国家重大基础研究专项基金资助项目 2003-03-01 2021-04-01 3