有限群的群代数的单形上幂级数映射的遍历性
Ergodicity of power series-map on the simplex of group algebra of a finite group
摘要：
研究了有限群$G$及其在实数域上的群代数$R[G]$，任意幂级数$p(t)= a_0+a_1t+ a_{2}t^{2}+ ...$，其中$ a_i \geq 0$，$a_0+a_1+ a_{2}+...= 1$，以及单纯形$$ S= \{x=\sum_{g\in G}x_gg\in R[G]: \sum_{g\in G}x_g=1, x_g\geq 0 {for any}\quad g\in G \}$$.示出了映射$p: S\to S$（其中$p(x)= a_0+a_1x+ a_{2}x^{2}+ >...$用于$x\in S$）在$S$上的遍历性。研究了该映射在给定点$x\in S $的正则性。
英文摘要：
A finite group $G$, its group algebra $R[G]$ over the field of real numbers, any power series $p(t)= a_0+a_1t+ a_{2}t^{2}+ ...$, where $ a_i \geq 0$, and $a_0+a_1+ a_{2}+...= 1$, and simplex $$ S= \{x=\sum_{g\in G}x_gg\in R[G]: \sum_{g\in G}x_g=1, x_g\geq 0 {for any}\quad g\in G \}$$ are considered. Ergodicity of the map $p: S\to S$, where $p(x)= a_0+a_1x+ a_{2}x^{2}+ >...$ for $x\in S$, on $S$ is shown. The regularity of this map at a given point $x\in S $ is investigated as well.
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