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

الأصل · EN

Let β>1 be a real number and M: R→ GL(ᵈ) be a uniformly almost periodic matrix-valued function. We study the asymptotic behavior of the product Pₙ(x) =M(βⁿ⁻¹x)... M(βx) M(x). Under some condition 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 β is a Pisot--Vijayaraghavan number is well studied.