Fully Developed Chaos in One-Dimensional Discrete Processes
It has turned out in recent years that dissipative dynamical systems exhibiting chaotic motion can often be modelled by one-dimensional maps, xn+1 = f(xn), where f(x) is typically a single hump function. An important feature of such maps in the chaotic region is the sensitivity to the change of the usual bifurcation parameter. One can introduce, however, parameters specifying the map, whose variation (at least within a certain range) does not destroy the chaotic state and leads to smooth parameter dependence of the statistical properties. As an example for such family of maps fully developed chaotic 1–0 maps are considered, which generate ergodic processes on an interval mapped everywhere two-to-one onto itself.
- P. Szepfalusy, G. Györgyi: to be publishedGoogle Scholar