  Chaotic scattering is a manifestation of transient chaos realized by the
scattering with non-integrable potential. When the initial position is taken in
the potential, a particle initially exhibits chaotic motion, but escapes
outside after a certain period of time. The time to stay inside the potential
can be seen as lifetime and this escape process may be regarded as a kind of
instability. The process of this type exists in the
Banks-Fischler-Shenker-Susskind (BFSS) matrix model in which the potential has
flat directions. We discuss this chaotic instability by reducing the system
with an ansatz to a simple dynamical system and present the associated fractal
structure. We also show the singular behavior of the time delay function and
compute the fractal dimension. This chaotic instability is the basic mechanism
by which membranes are unstable, which is also common to supermembranes at
quantum level.
