Chaotic foldings

In this paper we introduce the nomenclature and concept of chaotic foldings. We distinguish three types of folds; regular, chaotic and noisy. Here we argue that these three cases show up distinctly in the distribution of the lengths of the folds. In the regular case we have line distribution with complete absence of background. In the chaotic case, all length scales are involved. However, the distribution peaks sharply only at a few values of fold lengths implying the dominance of these length scales. Finally, in the case of noise, all length scales are involved without any dominant scale: there exists only a single broad peak. We argue that the emergence of dominant length scales in the case of chaotic folds is due to the existence of a dense set of periodic orbits in the phase space with differing stability indices. No such structure exists for a purely noisy system. We expect this work to have some applications in the studies of naturally occuring folded systems.