Dynamics of Higgs fields and a route to turbulence in the theory of SU(2) Yang-Mills fields

The dynamics of SU(2) Yancy-Mills (YM) fields, both free fields and fields interacting with Higgs bosons, is investigated by the Poincare surface-of-section method and the method of Lyapunov maximum exponents. As for free YM fields and YM fields interacting with a Higgs condensate, the route to turbulence in the system consisting of YM fields and Higgs particles lies through an infinite sequence of period-doubling bifurcations of the relevant phase trajectory. Prospects for future investigations in this field, such as constructing a consistent dynamical theory of second-order phase transitions on the basis of the analog between such transitions and the bifurcation transition to chaos, and taking into account the effects of the quark degrees of freedom of hadron matter and of thermal and quantum vacuum fluctuations on the scenario of the development of turbulence in the theory of YM fields, are also discussed. 14 refs., 1 fig.