  In this short review we propose a critical assessment of the role of chaos
for the thermalization of Hamiltonian systems with high dimensionality. We
discuss this problem for both classical and quantum systems. A comparison is
made between the two situations: some examples from recent and past literature
are presented which support the point of view that chaos is not necessary for
thermalization. Finally, we suggest that a close analogy holds between the role
played by Kinchin's theorem for high-dimensional classical systems and the role
played by Von Neumann's theorem for many-body quantum systems.
