The period of sequences generated by tent-like maps

摘要

In brief, we describe how to use knowledge about the sequence period generated by the linear multiplicative congruential generator of pseudorandom number sequences to determine the sequence period generated by continuous piecewise-linear chaotic maps of the unit interval or by maps topologically conjugate to these maps. The method exploits a relation between a continuous piecewise-linear map and a piecewise-linear but noncontinuous map of the unit interval with uniformly distributed extrema points, as well as the fact that the latter map can be considered as the generalization of the map describing the linear multiplicative congruential generator