  We investigate the dynamics of highly polydispersed finite granular chains.
From the spatio-spectral properties of small vibrations, we identify which
particular single-particle displacements lead to energy localization. Then, we
address a fundamental question: Do granular nonlinearities lead to chaotic
dynamics and if so, does chaos destroy this energy localization? Our numerical
simulations show that for moderate nonlinearities, although the overall system
behaves chaotically, it can exhibit long lasting energy localization for
particular single particle excitations. On the other hand, for sufficiently
strong nonlinearities, connected with contact breaking, the granular chain
reaches energy equipartition and an equilibrium chaotic state, independent of
the initial position excitation.
