the transfer of energy towards small scales) is high enough, the system relaxes to a time independent state with Kolmogorov scaling properties. As Obukhov-like interactions (favouring on the contrary the backflow of energy towards large scales) take over, the system transits through a Ruelle-Takens scenario into a chaotic state with stochastic fluctuations. There is clearly multifractality close to the transition, even if it looks less pronounced than the one observed in the GOY model for usual values of parameters.\
We switch to more deterministic concerns in the second part of this paper, which aims at characterizing singular fluctuations able to form in the ON model or more generally in any one-dimensional shell model. We shall argue that self-similar or soliton-like solutions of the equations of motion in the inertial range are the building blocks of intermittency, while movable singularities occuring at complex times induce chaos by inhibiting the energy cascade. We are not aware of any previous study of the structure of complex time singularities in shell models. In contrast, self-similar solutions were already considered within the context of the ON model by Siggia [@S78] and later on in more details by Nakano [@N88]. They are curiously absent of more 