Absolute continuity of the distribution of some Markov geometric series

Let （■）≥0 be the Markov chain of two states with respect to the probability measure of the maximal entropy on the subshift spaceΣdefined by Fibonacci incident matrix A.We consider the measureμof the probability distribution of the random seriesΣ■λ（0<λ<1）.It is proved thatμis singular ifλ∈(0,(5-1)/2) and thatμis absolutely continuous for almost allλ∈((5-1)/2,0.739).