有限性性质的稳定性判据及Barabanov范数的唯一性
Criteria for the stability of the finiteness property and for the uniqueness of Barabanov norms
AI总结：
本文给出有限不可约矩阵集满足有限性性质的稳定条件，并证明Barabanov范数在标量乘法下唯一的条件及其在小扰动下的持久性。
摘要：
如果一个矩阵集合中长矩阵乘积的最大指数增长率由周期乘积实现，则称该集合具有有限性性质。有限性性质在有限矩阵集中的普遍程度是当前研究的热点。本文给出了一个有限不可约矩阵集的条件，该条件不仅保证该集合具有有限性性质，而且保证所有足够接近的等基数集合也具有该性质。我们还证明了一个定理，给出了与有限不可约矩阵集相关的Barabanov范数在标量乘法下唯一的条件，并表明在某些情况下这些条件在小扰动下也是持久的。
英文摘要：
A set of matrices is said to have the finiteness property if the maximal rate of exponential growth of long products of matrices drawn from that set is realised by a periodic product. The extent to which the finiteness property is prevalent among finite sets of matrices is the subject of ongoing research. In this article we give a condition on a finite irreducible set of matrices which guarantees that the finiteness property holds not only for that set, but also for all sufficiently nearby sets of equal cardinality. We also prove a theorem giving conditions under which the Barabanov norm associated to a finite irreducible set of matrices is unique up to multiplication by a scalar, and show that in certain cases these conditions are also persistent under small perturbations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
