Random mappings with a single absorbing center and combinatorics of discretizations of the logistic mapping
This paper studies some properties of random mappings with a single absorbing center and applies them to several discretizations of the logistic mapping. In the first part of the paper, after introducing auxiliary notations, the continuous limit of several distributions as well as estimates are proved. Next the authors introduce the concept of absorbing center as a set such that once a trajectory enters this set it cannot leave it, noting that random mappings with an absorbing center are similar to mappings with a single attracting center. Then some results on the distributions of basins of attractions and the cycle lengths are established. Finally these results are applied to discretizations of the logistic map explaining some phenomena that occur in computer simulation of this dynamical system.
scientific article; zbMATH DE number 1383841