فهرست نشریات علمی دسترسی آزاد ایران

In this paper we consider the family fa(x) = axd(x − 1) + x when a < 0 is a real number and d ≥ 2 is an even integer. The function fa has a unique positive critical point. By decreasing the parameter a, the behavior of the orbit of this critical point changes. In this paper we consider two cases. In the first case the orbit of the positive critical point converges to 0 and in the second case the positive critical point is mapped to a repelling periodic point of period 2. In each case we give a recursive formula to determine the number of the periodic points of fa. Also, in each case we introduce an invariant set on which fa is chaotic. We employ conjugacy map and symbolic dynamics in our investigations.