  We improve on the description of the relationship that exists between
critical clusters in thermal systems and intermittency near the onset of chaos
in low-dimensional systems. We make use of the statistical-mechanical language
of inhomogeneous systems and of the renormalization group (RG) method in
nonlinear dynamics to provide a more accurate, formal, approach to the subject.
The description of this remarkable correspondence encompasses, on the one hand,
the density functional formalism, where classical and quantum mechanical
analogues match the procedure for one-dimensional clusters, and, on the other,
the RG fixed-point map of functional compositions that captures the essential
dynamical behavior. We provide details of how the above-referred theoretical
approaches interrelate and discuss the implications of the correspondence
between the high-dimensional (degrees of freedom) phenomenon and
low-dimensional dynamics.
