Evolutions of Tubes under Operability Constraints

In this paper, we study the evolutions of tubes that can be regarded as set-valued maps with compact images from Rq to a finite dimensional vector space X under some constraints that we call operability constraints. We first recall some proper- ties of the mutational calculus in the metric space K X., oI. where K X. is the set of nonempty compact subsets of X, and oI is the Hausdorff distance. The main result is the geometric characterization of the dynamics of the tubes that satisfy the operability constraint.