Asymmetric Tent Map Expansions - II: Purely Periodic Points.

The family of asymmetric tent maps T sub (alpha); [0, 1] for alpha > is defined by T sub (alpha) (X = [alpha x for 0 = x = 1 over alpha, alpha over alpha - 1 (1 - x) for 1 over alpha = x = 1.]. Let Per(T sub (alpha)) and Fix(T sub (alpha)) denote the sets of eventually periodic points and purely periodic points under T sub (alpha), and let Per sub 0 (T sub (alpha)) = {x: T sup (k) sub (alpha) (x) = 0 for some k >=1}. Part I showed that for certain alpha, called special Pisot numbers, one has Per(T sub (alpha)) = Q(alpha) omega [0, 1]. Special Pisot numbers consist of alpha such that both alpha and alpha over alpha - 1 are Pisot numbers. This paper characterizes Fix(T sub (alpha)) and Per sub 0(T sub (alpha)) for most special Pisot numbers.