论文标题
非负矩阵产物的动力学
Dynamics of products of nonnegative matrices
论文作者
论文摘要
该手稿的目的是了解非负矩阵产品的动力学。我们扩展了Perron-Frobenius定理对非负矩阵的周期点的众所周知的结果，以与有限的许多与单词相关的非负矩阵以及随后与单词相关的非负矩阵产品相关的产品，可能是无限长度。我们还利用了指数映射的适当定义和$ \ mathbb {r}^{n} $的正骨上的对数图，并探索通过上述函数定义的某些亚均匀图的周期点之间的关系，如上所述。
The aim of this manuscript is to understand the dynamics of products of nonnegative matrices. We extend a well known consequence of the Perron-Frobenius theorem on the periodic points of a nonnegative matrix to products of finitely many nonnegative matrices associated to a word and later to products of nonnegative matrices associated to a word, possibly of infinite length. We also make use of an appropriate definition of the exponential map and the logarithm map on the positive orthant of $\mathbb{R}^{n}$ and explore the relationship between the periodic points of certain subhomogeneous maps defined through the above functions and the periodic points of matrix products, mentioned above.
