  I investigate contractions via Kac-Moody formalism. In particular, I show how
the symmetry algebra of the standard 2-D Kepler system, which was identified by
Daboul and Slodowy as an infinite-dimensional Kac-Moody loop algebra, and was
denoted by ${\mathbb H}_2 $, gets reduced by the symmetry breaking term,
defined by the Hamiltonian \[ H(\beta)= \frac 1 {2m} (p_1^2+p_2^2)- \frac
\alpha r - \beta r^{-1/2} \cos ((\phi-\gamma)/2). \] For this $H (\beta)$ I
define two symmetry loop algebras ${\mathfrak L}_{i}(\beta), i=1,2$, by
choosing the `basic generators' differently. These ${\mathfrak L}_{i}(\beta)$
can be mapped isomorphically onto subalgebras of ${\mathbb H}_2 $, of
codimension 2 or 3, revealing the reduction of symmetry. Both factor algebras
${\mathfrak L}_i(\beta)/I_i(E,\beta)$, relative to the corresponding
energy-dependent ideals $I_i(E,\beta)$, are isomorphic to ${\mathfrak so}(3)$
and ${\mathfrak so}(2,1)$ for $E<0$ and $E>0$, respectively, just as for the
pure Kepler case. However, they yield two different non-standard contractions
as $E \to 0$, namely to the Heisenberg-Weyl algebra ${\mathfrak h}_3={\mathfrak
w}_1$ or to an abelian Lie algebra, instead of the Euclidean algebra
${\mathfrak e}(2)$ for the pure Kepler case. The above example suggests a
general procedure for defining generalized contractions, and also illustrates
the {\em `deformation contraction hysteresis'}, where contraction which involve
two contraction parameters can yield different contracted algebras, if the
limits are carried out in different order.
