# Ergodicity of power series-maps on the simplexes of group algebras of finite groups

Bekbaev, Ural and Mohamat Johari, Mohamat Aidil (2017) Ergodicity of power series-maps on the simplexes of group algebras of finite groups. In: 4th International Conference on Mathematical Applications in Engineering (ICMAE ’17), 8th-9th Aug. 2017, Kuala Lumpur, Malaysia.

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## Abstract

For every finite group $G$ the ergodicity of any map $p: S\rightarrow S$ on $S$ is shown, where $\mathcal{R}[G]$ is the real group algebra of $G$ , $$S= \{x=\sum_{g\in G}x_gg\in \mathcal{R}[G]: \sum_{g\in G}x_g=1, x_g\geq 0 \mbox{ for any}\quad g\in G\}-\mbox{the simplex,}$$ $p(x)= a_0+a_1x+ a_{2}x^{2}+ ...$, \ $x\in S$,\ $a_i\geq 0$ and $\sum_{i=0}^{\infty}a_i=1$. The regularity of this map at a given point $x\in S$ is investigated as well.

Item Type: Conference or Workshop Item (Plenary Papers) 6830/61353 power series-maps Q Science > QA MathematicsQ Science > QA Mathematics > QA300 Analysis Kulliyyah of Engineering > Department of Science Associate Prof. Ural Bekbaev 16 Jan 2018 11:08 18 Oct 2018 08:55 http://irep.iium.edu.my/id/eprint/61353