A Rapidly-converging Lower Bound for the Joint Spectral Radius via Multiplicative Ergodic Theory
نویسنده
چکیده
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. MSC primary 15A18, 37H15, 65F15, secondary 37M25.
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تاریخ انتشار 2009