  The paper analyzes the structure and the inner long-term dynamics of the
invariant compact sets for the skewproduct flow induced by a family of
time-dependent ordinary differential equations of nonhomogeneous linear
dissipative type. The main assumptions are made on the dissipative term and on
the homogeneous linear term of the equations. The rich casuistic includes the
uniform stability of the invariant compact sets, as well as the presence of
Li-Yorke chaos and Auslander-Yorke chaos inside the attractor.
