  We analyze the stability of the geodesic curves in the geometry of the
Gibbons-Maeda-Garfinkle-Horowitz-Strominger black hole, describing the space
time of a charged black hole in the low energy limit of the string theory. The
stability analysis is performed by using both the linear (Lyapunov) stability
method, as well as the notion of Jacobi stability, based on the
Kosambi-Cartan-Chern theory. Brief reviews of the two stability methods are
also presented. After obtaining the geodesic equations in spherical symmetry,
we reformulate them as a two-dimensional dynamic system. The Jacobi stability
analysis of the geodesic equations is performed by considering the important
geometric invariants that can be used for the description of this system (the
nonlinear and the Berwald connections), as well as the deviation curvature
tensor, respectively. The characteristic values of the deviation curvature
tensor are specifically calculated, as given by the second derivative of
effective potential of the geodesic motion. The Lyapunov stability analysis
leads to the same results. Hence, we can conclude that in the particular case
of the geodesic motion on circular orbits in the
Gibbons-Maeda-Garfinkle-Horowitz-Strominger, the Lyapunov and the Jacobi
stability analysis gives equivalent results.
