Periodic Orbits of the Logistic Map in Single and Double Precision Implementations

In finite precision implementations of chaotic maps all trajectories are eventually periodic. The goal of this brief is to develop methods for systematic study of effects of finite precision computations on dynamical behaviors of discrete maps and to carry out a study of the logistic map in this context. In particular, we are interested in finding all cycles when the logistic map is implemented in single and double precision and studying properties of these cycles including the size of the basin of attraction, and the maximum and average convergence times.