A rapidly-converging lower bound for the joint spectral radius via multiplicative ergodic theory
A rapidly-converging lower bound for the joint spectral radius via multiplicative ergodic theory
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DOI：
10.1016/j.aim.2010.06.008
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发表时间：
2009-06
影响因子：
1.7
通讯作者：
I. Morris
中科院分区：
文献类型：
--
作者：
I. Morris
我们使用遍历理论来证明 M.A. Berger 和 Y. Wang 定理的定量版本，该定理将一组矩阵的联合谱半径与这些矩阵的有限乘积的谱半径联系起来。证明基于最小同胚上的连续矩阵余循环的结构定理，该定理具有所有前向积一致有界的性质。
We use ergodic theory to prove a quantitative version of a theorem of M.A. Berger and Y. Wang, which relates the joint spectral radius of a set of matrices to the spectral radii of finite products of those matrices. The proof rests on a structure theorem for continuous matrix cocycles over minimal homeomorphisms having the property that all forward products are uniformly bounded.