Design of piecewise-linear Markov maps generating white chaos: an inverse problem of dynamical systems

Discusses the design of a discrete dynamical system generating chaos with a white spectrum. This chaos is referred to as white chaos. The results on the design of a piecewise-linear Markov map generating white chaos are summarized. For any number of subintervals of maps, maps always exist if the rank of the incident matrix is equal to 1. However, no piecewise linear Markov map whose incident matrix's rank is equal to 1 can generate white chaos whose higher-order power spectra are also uniform. (2) The following conjecture is obtained. The number of subintervals of maps is not less than two times as many as the rank of the incident matrix. Several concrete examples are included