  A rather complete phenomenology of the singularities is developed according
to a new algebraic point of view in the frame of Langlands global
correspondences. That is to say,a process of: -singularizations and versal
deformations of these, -singularizations and monodromies of these, is envisaged
on all the sections of sheaves of differentiable (bi)functions on (bi)linear
algebraic (semi)groups constituting the n-dimensional representations of the
global Weil groups. To get the searched holomorphic and cuspidal
representations,it is necessary to consider: -the resolutions of the
singularities and the blowups of the versal deformations; -the resolutions of
the singularities in the monodromy cases. Furthermore, the geometry of the
versal deformations and of their blowups is studied, as well as the associated
dynamics leading to the consideration of singular hyperbolic attractors and of
singular strange attractors.
