Analytical Solutions to Multivalued Maps

Abstract

We present explicit solutions for a class of chaotic maps. The return-maps generated by a special class of chaotic functions can be multivalued, or even they can represent an erratic set of points. In some cases the produced time series can have an increasing time-dependent maximum Lyapunov exponent. We discuss some applications of the obtained results. In particular, we present a chaotic lattice model for the investigation of the propagation of carriers in the presence of disorder.