| Title | Products of non-stationary random matrices and multiperiodic equations of several scaling factors |
| Authors | AH Fan, B Saussol, Jörg Schmeling |
| Alternative Location | http://pjm.math.berkeley.ed..., Restricted Access |
| Publication | Pacific Journal of Mathematics |
| Year | 2004 |
| Volume | 214 |
| Issue | 1 |
| Pages | 31 - 54 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Pacific Journal of Mathematics |
| Abstract 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. |
| ISBN/ISSN/Other | ISSN: 0030-8730 |
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