Cell Mapping for Random Transformations

The method of Cell Mapping is a numerical tool to analyze the long-term behavior of dynamical systems. For deterministic systems, which are described by nonsingular transformations, Cell Mapping is characterized by a certain discretization of the Frobenius–Perron operator first proposed by Ulam 3]. Our purpose is to extend the concept to dynamical systems which are generated by random transformations. At this, time evolution of absolutely continuous measures and the corresponding densities will be described by Markov operators whose fixed points refer to invariant measures and densities respectively. A discretization of the Markov operator on densities leads directly to the reformulation of Cell Mapping in the stochastic context. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)