Random mappings with a single absorbing center and combinatorics of discretizations of the logistic mapping

Abstract

Distributions of basic characteristics of random mappings with a single absorbing center are calculated. Results explain some phenomena occurring in computer simulations of the logistic mapping.

The asymptotic behavior of elementary symmetric functions on a probability distribution

“…where (7, z) is the entire analytic function defined by the infinite product (6) k_ (k_ l) I _k"/-(k-1)"/ } 7 ze z (7) the following representation and for the values xl < ForO<7< is also valid.…”