Recurrence of matrix cocycles

This paper considers measurable cocycles with values in the subgroup of SL (2, ℂ) of diagonal and skew-diagonal matrices over an ergodic transformation preserving the probability measure. We prove the recurrence of such cocycles under certain conditions as well as the equivalence of two definitions...

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Bibliographic Details
Published in:Moscow University mathematics bulletin 2010-10, Vol.65 (5), p.217-219
Main Author: Lipatov, M. E.
Format: Article
Language:English
Subjects:
Analysis
Brief Communications
Mathematics
Mathematics and Statistics
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Summary:This paper considers measurable cocycles with values in the subgroup of SL (2, ℂ) of diagonal and skew-diagonal matrices over an ergodic transformation preserving the probability measure. We prove the recurrence of such cocycles under certain conditions as well as the equivalence of two definitions of the recurrence.
ISSN:0027-1322
1934-8444
DOI:10.3103/S0027132210050086