  In this paper, we investigate the influence of the angular momentum of a
charged particle around non-extremal and extremal
Einstein-Maxwell-Dilaton-Axion black holes on the Lyapunov exponent. The
angular momentum's ranges and spatial regions where the bound of the exponent
is violated are found for certain values of the rotation parameter and
dilatonic constant of the black holes. This violation always exists when the
rotation parameter is large enough and the rotation directions of the particle
is opposite to those of the black holes. The spatial regions outside the
extermal black hole for the violation is relatively large. In the near-horizon
regions of the extremal black holes, the violation depends on the rotation
directions of the black holes and particle, and does not depend on the value of
the angular momentum.
