Analysis of chaotic motion and its shape dependence in a generalized piecewise linear map

We analyze the chaotic motion and its shape dependence in a piecewise linear map using Fujisaka's characteristic function method. The map is a generalization of the one introduced by Artuso. Exact expressions for diffusion coefficients are obtained with previously obtained results used as special cases. A fluctuation spectrum relating to the probability density function is obtained in a parametric form. We also give limiting forms of the above quantities. The dependence of the diffusion coefficient and probability density function on the shape of the map is examined.