Study on the properties of chaotic control map

In all chaotic function maps the most typical map is Tent map. It has extremely complicated dynamical system behavior. It is found that this simplest parabola map contains modern chaos theory. In this paper, we mainly study the generalized Tent map. First we give the definition of the probability density functions on [0,1], and then study the orbits of the probability density functions by the control of a generalized Tent map. At last, we obtain that the orbit converges to a fixed probability density function in L¹(X).