Klemm, A.; Pokrovskij, A. Random mappings with a single absorbing center and combinatorics of discretizations of the logistic mapping. (English) Zbl 0937.37012 J. Appl. Math. Stochastic Anal. 12, No. 3, 205-221 (1999). 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. Reviewer: M.Calvo (Zaragoza) Cited in 1 Document MSC: 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 65P20 Numerical chaos 37H10 Generation, random and stochastic difference and differential equations 37E05 Dynamical systems involving maps of the interval Keywords:random mappings; discretization of logistic map; chaotic numerics; absorbing center; logistic mapping; attracting center; basins of attractions PDFBibTeX XMLCite \textit{A. Klemm} and \textit{A. Pokrovskij}, J. Appl. Math. Stochastic Anal. 12, No. 3, 205--221 (1999; Zbl 0937.37012) Full Text: DOI EuDML