Ergodicity of power series-maps on the simplexes of group algebras of finite groups
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...
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Main Authors: | , |
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Format: | Conference or Workshop Item |
Language: | English English |
Published: |
IOP Publishing
2017
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Subjects: | |
Online Access: | http://irep.iium.edu.my/61353/1/61353_Ergodicity%20of%20power%20series-maps.pdf http://irep.iium.edu.my/61353/7/61353_Ergodicity%20of%20power%20series-maps%20on%20the%20simplexes%20of%20group_scopus.pdf http://irep.iium.edu.my/61353/ http://iopscience.iop.org/article/10.1088/1742-6596/949/1/012023 |
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Summary: | 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. |
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