  For affine control systems with bounded control range the control sets, i.e.,
the maximal subsets of complete approximate controllability, are studied using
spectral properties. For hyperbolic systems there is a unique control set with
nonvoid interior and it is bounded. For nonhyperbolic systems, these control
sets are unbounded. In an appropriate compactification of the state space there
is a unique chain control set and the relations to the homogenous part of the
control system are worked out.
