Unique ergodicity and random matrix products
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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \...
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| Format: | Book Chapter |
| Language: | eng |
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| Online Access: | Get full text |
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| Summary: | 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 \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\frac{1}{n}\log (||\mathop \Pi \limits_{i = 0}^{n - 1} B (T^i x)||)$$\end{document} 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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| ISSN: | 0075-8434 1617-9692 |