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

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.