Iterations of tent maps

Abstract:

As a basic class of non-linear maps, tent maps is famous for their periodic point problem. And tent maps vertices as the points breaking the monotonicity in iterations have their own rules. This paper focuses on the change of the tent maps number of vertices under iterations, and gives the formula for the number of vertices in the specific case of parameter a=0.5,b=(1+√5)/4 and then the formula of the number of n-period points is given when b=1.