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arXiv · 0906.0260

A rapidly-converging lower bound for the joint spectral radius via multiplicative ergodic theory

Ian D. Morris
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Abstract

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 theorem asserting the existence of a continuous invariant splitting for certain matrix cocycles defined over a minimal homeomorphism and having the property that all forward products are uniformly bounded.

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Ian D. Morris. 2009-06-01. A rapidly-converging lower bound for the joint spectral radius via multiplicative ergodic theory. https://arxiv.org/abs/0906.0260

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