A rapidly-converging lower bound for the joint spectral radius via multiplicative ergodic theory
Provides a theoretical advance in computing joint spectral radius, relevant to researchers in dynamical systems and control theory.
The authors prove a quantitative version of a theorem relating the joint spectral radius of a set of matrices to spectral radii of finite products, using ergodic theory to establish a continuous invariant splitting for certain matrix cocycles.
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.