On the spectrum of the transfer operators of a one-parameter family with intermittency transition

We study the transfer operators for a family $F_r:[0,1]\to [0,1]$ depending on the parameter $r\in [0,1]$, which interpolates between the tent map and the Farey map. In particular, considering the action of the transfer operator on a suitable Hilbert space, we can define a family of infinite matrices associated to the operators and study their spectrum by numerical methods.