Period doubling and multifractals in 1-D iterative maps (Q1208390)

In the paper, the period doubling solutions of one-dimensional iterative maps and their chaotic fractality based on a similar structure approach are discussed. The authors offer a highly accurate method to compute the period doubling bifurcation solutions of a general one-dimensional iterative map. Section two outlines the construction and analysis of the similar structure of period doubling solutions and introduces specific period doubled factors. In Section three, a discussion of the fractality of the one-dimensional map in period doubling leading to chaos is presented; and several generalized fractal dimensions are given. Section four shows an example to demonstrate the procedure.