  We discuss how iterative solutions of QCD inspired gap-equations at finite
chemical potential show domains of chaotic behavior as well as non-chaotic
domains which represent one or the other of the only two -- usually distinct --
positive mass gap solutions with broken or restored chiral symmetry,
respectively. In the iterative approach gap solutions exist which exhibit
restored chiral symmetry beyond a certain dynamical cut-off energy. A chirally
broken, non-chaotic domain with no emergent mass poles and hence with no
quasi-particle excitations exists below this energy cutoff. The transition
domain between these two energy separated domains is chaotic. As a result, the
dispersion relation is that of quarks with restored chiral symmetry, cut at a
dynamical energy scale, determined by fractal structures. We argue that the
chaotic origin of the infrared cut-off could hint at a chaotic nature of
confinement and the deconfinement phase transition.
