LIMIT-CYCLES IN A QUADRATIC DISCRETE ITERATION

I study the truncated logistic equation as a map of D integers. The number of limit cycles and the size of longest cycle are averaged exhaustively over many values of D for parameter values a beyond the first accumulation point. Fits of these quantities are compared with estimates obtained from random maps; the results suggest some form of self-organization. I also present some analytical results on the existence and position of fixed points and a fast matrix method to enumerate limit cycles of arbitrary length for given a and D.