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 0024-6107

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Abstract

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
ISSN:	0024-6107
Date:	October 1997
Volume:	56
Number:	Part 2
Number of Pages:	10
Page Range:	pp. 395-404
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/15903

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