Maximum Lyapunov exponent of highly excited finite systems

In this communication we analyze the behavior of the maximum global Lyapunov exponent (MGLE) and the maximum local Lyapunov exponent (MLLE) for highly excited two- and three-dimensional finite systems which undergo a fragmentation process. We relate the behavior of the MGLE with the caloric curve of the two-dimensional disks, and we relate the asymptotic fluctuations in the MLLE to the appearance of a power law spectra in the fragmentation of 3D drops.