ORDER-CHAOS TRANSITIONS IN-FIELD THEORIES WITH TOPOLOGICAL TERMS - A DYNAMICAL-SYSTEMS APPROACH

We present a comparative study of the dynamical behaviour of topologic al systems of recent interest, namely the non-Abelian Chern-Simons Hig gs system and the Yang-Mills Chem-Simons Higgs system. By reducing the full field theories to temporal differential systems by using the ass umption of spatially homogeneous fields, we study the Lyapunov exponen ts for two types of initial conditions. We also examine in minute deta il the behaviour of the Lyapunov spectra as a function of the various coupling parameters in the system. We compare our results with those f or Abelian Higgs, Yang-Mills Higgs and Yang-Mills Chern-Simons systems which have been discussed recently by other authors. The role of the various terms in the Hamiltonians for such systems in determining the order-disorder transitions is emphasized and shown to be counter-intui tive in the Yang-Mills Chern-Simons Higgs systems.