  The Zeeman splitting of localized electrons in a quantum dot in the Kondo
regime is studied using a new slave-boson formulation. Our results show that
the Kondo peak splitting depends on the gate potential applied to the quantum
dot and on the topology of the system. A common fact of any geometry is that
the differential susceptibility shows a strong non linear behavior. It was
shown that there exist a critical field above which the Kondo resonance is
splitted out. This critical field rapidly diminishes when the gate potential is
lowered, as a consequence of the reduction of the Kondo temperature and a
subsequent strong enhancement in the differential susceptibility occurring at
low fields. The critical field is also strong depedent on the topology of the
circuit. Above this critical field the Zeeman splitting depends linearly upon
the magnetic field and does not extrapolate to zero at zero field. The
magnitude of the Y-intercept coordinate depends on the gate potential but the
slope of this function is not renormalized being independent of the value of
the gate potential. Our results are in agreement with very recent experiments.
