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arXiv · 2010.05560

Dynamics of products of nonnegative matrices

Sachindranath Jayaraman·Yogesh Kumar Prajapaty·Shrihari Sridharan
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Abstract

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.

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Sachindranath Jayaraman, Yogesh Kumar Prajapaty, Shrihari Sridharan. 2020-10-12. Dynamics of products of nonnegative matrices. https://arxiv.org/abs/2010.05560

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