  In this paper we develop a groupoid approach to some basic topological
properties of dual spaces of solvable Lie groups using suitable dynamical
systems related to the coadjoint action. One of our main results is that the
coadjoint dynamical system of any exponential solvable Lie group is a piecewise
pullback of group bundles. Our dynamical system approach to solvable Lie groups
also allows us to construct some new examples of connected solvable Lie groups
whose $C^*$-algebras admit faithful irreducible representations.
