This paper deals with the problem of characterizing the set of states reachable in arbitrary small
time (the set ``A'') for bilinear control systems whose state varies
on a compact Lie group. The paper was motivated
by the desire of generalizing the results of [QC2] to any system on a compact Lie group. Even if the
system is controllable the set A may not be the whole Lie group and can in some cases be empty. In
fact, a sufficient condition is given in the paper for this set to be empty. A characterization of
this set as a Lie subgroup of the underlying Lie group is given under suitable assumptions and its
properties are related to the Small Time Local Controllability of the identity of the group. A scheme
is presented for the study of the set A which relies only on the property of the Lie algebra of the
underlying Lie group. This was in fact the scheme that was used in [QC2] for the study of the
controllability properties of quantum bits. The paper, uses this scheme to generalize the results of
[QC2] to spin systems with value of the spin different from 1/2.
The following article has been accepted by Journal of Mathematical Physics.
After it is published, it will be found at