  We apply a variant of the Nose-Hoover thermostat to derive the Hamiltonian of
a nonextensive system that is compatible with the canonical ensemble of the
generalized thermostatistics of Tsallis. This microdynamical approach provides
a deterministic connection between the generalized nonextensive entropy and
power law behavior. For the case of a simple one-dimensional harmonic
oscillator, we confirm by numerical simulation of the dynamics that the
distribution of energy H follows precisely the canonical q-statistics for
different values of the parameter q. The approach is further tested for
classical many-particle systems by means of molecular dynamics simulations. The
results indicate that the intrinsic nonlinear features of the nonextensive
formalism are capable to generate energy fluctuations that obey anomalous
probability laws. For q<1 a broad distribution of energy is observed, while for
q>1 the resulting distribution is confined to a compact support.
