Maximal cycle length of pseudochaotic sequences generated by piecewise linear maps

Abstract

In the paper we consider the maximal cycle length of pseudochaotic sequences generated by piecewise linear maps of the unit interval. We define two families of piecewise linear maps: piecewise linear noncontinuous maps (sawtooth maps) and piecewise linear continuous maps (tent-like maps). We formulate and prove an equation relating both families of maps. We show also that there may exist a dependence between the cycle length of sequences generated by sawtooth maps and the cycle length of sequences obtained for tent-like maps for the same value of a parameter and the same initial point.