Skew products of shifts with a compact Lie group
UNSPECIFIED. (1997) Skew products of shifts with a compact Lie group. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 56 (Part 2). pp. 395-404. ISSN 0024-6107Full text not available from this repository.
We consider aperiodic shifts of finite type sigma with an equilibrium state m and associated skew-products sigma(f) where f:X --> G is Holder and G is a compact Lie group. We show that generically sigma(f) is weak-mixing and give constructive methods for achieving weak-mixing by perturbing an arbitrary f at a finite number of small neighbourhoods. When sigma(f) is not ergodic we describe the (closed) ergodic decomposition precisely. The key result shows that certain measurable eigenfunctions are essentially Holder continuous. This leads to conditions for weak-mixing or ergodicity in terms of a functional equation which involves Holder rather than measurable functions.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Journal or Publication Title:||JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES|
|Publisher:||LONDON MATH SOC|
|Number of Pages:||10|
|Page Range:||pp. 395-404|
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