Asymmetric tent map expansions II. Purely periodic points

where /3 a/(a 1) and the nonnegative integers ni are specified by the itinerary I(x)= L"RLnRLn..., which encodes the successive iterates T(’)(x) as being in the left interval [0, 1/a] (labelled L) or the half-open right interval (1/a, 1] (labelled R). For certain x the expansion (1.2) contains only finitely many R’s, and the corresponding itinerary is then I(x) L"oR RnRL; these numbers x are exactly the preperiodic points of 0, denoted Per0(T,). Part I studied the set Per(T) of the eventually periodic points of T and proved that for certain values of a, called special Pisot numbers, one has