Abstract
We investigate the question: if T:X → X is a uniquely ergodic homeomorphism of a compact metrizable space and B:X → GL(k,R) is a continuous map of X into the space of invertible, k × k, real matrices does \(\frac{1}{n}\log (||\mathop \Pi \limits_{i = 0}^{n - 1} B (T^i x)||)\) converge uniformly to a constant? Conditions on B are given so that the answer is ‘yes’, and an example is given to show the general answer is ‘no’ when k≥2. The more general case of vector bundle automorphisms covering T is considered.
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© 1986 Springer-Verlag
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Walters, P. (1986). Unique ergodicity and random matrix products. In: Arnold, L., Wihstutz, V. (eds) Lyapunov Exponents. Lecture Notes in Mathematics, vol 1186. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076832
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DOI: https://doi.org/10.1007/BFb0076832
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