The perturbative method for discrete processes and its physical application
In this note chaotic iterations are considered which only slightly differ from processes of known properties. Averages are calculated in case of noisy perturbation of systems exhibiting originally a fixed point and where the iteration goes along a discrete one-dimensional chain or on the Cayley tree. As a physical example the disordered Ising model is considered on these lattices and results on spin fluctuations are presented. Finally, probabilistic properties of perturbed one-dimensional iterations are reviewed, where even the unperturbed systems show chaotic behaviour. For the latter ones in the examples the hat function and the logistic map in the fully developed chaotic state are taken, and we also discuss a noisy iteration describing a one-dimensional disordered quantum mechanical system.
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