Ergodicity of power series-maps on the simplexes of group algebras of finite groups - Bekbaev, Ural; Mohamat Johari, Mohamat Aidil (IOP Publishing, 2017)
For every finite group $G$ the ergodicity of any map $p: S→ S$ on $S$ is shown, where $\mathcal{R}[G]$ is the real group algebra of $G$ , $$ S= \{x=\sum_{g\in G}x_gg\in \mathcal{R}[G]: \sum_{g\in G}x_g=1, x_g≥ 0 for any\quad g\in G\}-the simplex, $$ $p(x)= a_0+a_1x+ a_{2}x^{2}+ ...$, \ $x\in S$,\ $a_i≥ 0$ and $\sum_{i=0}^{∞}a_i=1$. The regularity of this map at a given point $x\in S $ is investigated as well.