In his "Structural stability and morphogenesis", R. Thom (especially in the chapter about dynamics of forms) among other things speculates about a notion of complexity of a "form" (mapping between manifolds). He suggested the following definition -- it is a minimal number of intersections with a bifurcation set in a functional space of a path (deformation) joining this mapping with a ground mapping (the simplest one). The choice of this ground mapping is also an interesting question. He also discussed other possible notions of complexity.
So, I'm interesting if there any works in which these ideas develops in a rigorous mathematical way. And maybe other speculative ideas described in this book. (I'm familiar with singularity theory in general.)
p.s. I'm sorry for my English.
