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.

• Författare: AH Fan; B Saussol; Jörg Schmeling
• Avdelning/ar: Matematik LTH; Dynamical systems
• Publiceringsår: 2004
• Språk: Engelska
• Sidor: 31-54
• Publikation/Tidskrift/Serie: Pacific Journal of Mathematics
• Volym: 214
• Issue: 1
• Länkar: http://pjm.math.berkeley.edu/pjm/2004/214-1/p04.xhtml
• Dokumenttyp: Artikel i tidskrift
• Förlag: Pacific Journal of Mathematics
• Ämne: Mathematics
• Status: Published
• Forskningsgrupp: Dynamical systems
• ISBN/ISSN/Övrigt: ISSN: 0030-8730