  It is shown that the distributed chaos in the simple Hamiltonian
(conservative) dynamical systems, such as the Nose-Hoover oscillator and double
oscillator, can mimic the distributed chaos in the isotropic homogeneous
turbulence. Direct numerical simulations with the classic Toda lattice and with
the nonlinear Schr\"{o}dinger equation (soliton turbulence) under random
initial conditions have been also discussed in this context. These properties
of the distributed chaos have been related to analytical properties of the
Hamiltonian systems. Decrease of the smoothness results in the power-law
spectra instead of the stretched exponential ones characteristic to the
distributed chaos, both for the dynamical systems and for turbulence.
