Chaotic intermittency with non-differentiable M(x) function

One-dimensional maps showing chaotic intermittency with discontinuous reinjection probability density functions are studied. For these maps, the reinjection mechanism possesses two different processes.The M function methodology is applied to analyze the complete reinjection mechanism and to determine the discontinuous reinjection probability density function. In these maps the function M(x) is continuous and non -differentiable. Theoretical equations are found for the function M(x) and for the reinjection probability density function. Finally, the theoretical results are compared with numerical data finding high accuracy.