Products of non-stationary random matrices and multiperiodic equations of several scaling factors

Summary, in English

Let beta > 1 be a real number and M : R --> GL(C-d) be a uniformly almost periodic matrix-valued function. We study the asymptotic behavior of the product P-n(x) = M(beta(n-1)x)...M(betax) M(x). Under some conditions we prove a theorem of Furstenberg-Kesten type for such products of non-stationary random matrices. Theorems of Kingman and Oseledec type are also proved. The obtained results are applied to multiplicative functions defined by commensurable scaling factors. We get a positive answer to a Strichartz conjecture on the asymptotic behavior of such multiperiodic functions. The case where is a Pisot-Vijayaraghavan number is well studied.

• Author: AH Fan; B Saussol; Jörg Schmeling
• Department/s: Mathematics (Faculty of Engineering); Dynamical systems
• Publishing year: 2004
• Language: English
• Pages: 31-54
• Publication/Series: Pacific Journal of Mathematics
• Volume: 214
• Issue: 1
• Links: http://pjm.math.berkeley.edu/pjm/2004/214-1/p04.xhtml
• Document type: Journal article
• Publisher: Pacific Journal of Mathematics
• Topic: Mathematics
• Status: Published
• Research group: Dynamical systems
• ISBN/ISSN/Other: ISSN: 0030-8730