Abstract
Let L(theta, lambda) be the set of limit points of the fractional parts {lambda theta(n)}, n = 0, 1, 2, . . . , where theta is a Pisot number and lambda is an element of Q (theta). Using a description of L(theta, lambda), due to Dubickas, we show that there is a sequence (lambda(n))(n >= 0) of elements of Q(theta) such that Card (L(theta, lambda(n))) < Card (L(theta, lambda(n+1))), for all n >= 0. Also, we prove that the fractional parts of Pisot numbers, with a fixed degree greater than 1, are dense in the unit interval.