极值遍历测度与矩阵半群的有限性性质
动力系统
2011-07-04 v1 环与代数
摘要
设 \bS = { S 1 , . . . , S K } \bS=\{S_1,...,S_K\} \bS = { S 1 , ... , S K } d × d d\times d d × d Σ K + \varSigma_{K}^+ Σ K + i \bcdot : N → { 1 , . . . , K } i_{\bcdot}\colon\mathbb{N}\rightarrow\{1,...,K\} i \bcdot : N → { 1 , ... , K } θ : Σ K + → Σ K + ; i \bcdot ↦ i \bcdot + 1 \theta\colon\varSigma_{K}^+\rightarrow\varSigma_{K}^+;\ i_{\bcdot}\mapsto i_{\bcdot+1} θ : Σ K + → Σ K + ; i \bcdot ↦ i \bcdot + 1 μ ∗ \mu_* μ ∗ μ ∗ \mu_* μ ∗ i \bcdot ∈ Σ K + i_{\bcdot}\in\varSigma_{K}^+ i \bcdot ∈ Σ K + ρ ( \bS ) = lim n → ∞ \norm S i 1 . . . S i n n {\rho}(\bS)=\lim_{n\to\infty}\sqrt[n]{\norm{S_{i_1}...S_{i_n}}} ρ ( \bS ) = lim n → ∞ n \norm S i 1 ... S i n \bS \bS \bS ρ ( \bS ) \rho(\bS) ρ ( \bS ) \bS \bS \bS \bS \bS \bS ( i 1 , . . . , i n ) (i_1,...,i_n) ( i 1 , ... , i n ) ρ ( \bS ) = ρ ( S i 1 . . . S i n ) n \rho(\bS)=\sqrt[n]{\rho(S_{i_1}...S_{i_n})} ρ ( \bS ) = n ρ ( S i 1 ... S i n ) \bS \bS \bS μ ∗ \mu_* μ ∗ Σ K + \varSigma_{K}^+ Σ K + i \bcdot i_{\bcdot} i \bcdot
引用
@article{arxiv.1107.0123,
title = {Extremal ergodic measures and the finiteness property of matrix semigroups},
author = {Xiongping Dai and Yu Huang and Mingqing Xiao},
journal= {arXiv preprint arXiv:1107.0123},
year = {2011}
}
备注
9 pages; accepted by Proceedings of the AMS