Chaotic intermittency in maps with infinite derivative

This is the authors' abstract. We don't add key points for this paper.

The classical intermittency theory developed forty years ago considers a uniform reinjection probability density function (RPD). However, in the last ten years, studies have found a more general RPD, which depends on the type of prereinjection points, extreme or infinite derivative points. Recently, we have introduced an analytical scheme to estimate the non-uniform RPD when the pre-reinjection points are extreme. Here, this theoretical scheme is extended to embrace pre-reinjection points with infinite derivative. The proposed theoretical method, to get the RPD, needs only the explicit expression of the map, and it is general and direct to use. For different intermittency types and different non-linearity, the theoretical predictions show a very high agreement with the numerical results.