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We construct the most general form of axially symmetric SU(2)-Yang-Millsfields in Bianchi cosmologies. The dynamical evolution of axially symmetric YMfields in Bianchi I model is compared with the dynamical evolution of theelectromagnetic field in Bianchi I and the fully isotropic YM field inFriedmann-Robertson-Walker cosmologies. The stochastic properties of axiallysymmetric Bianchi I-Einstein-Yang-Mills systems are compared with those ofaxially symmetric YM fields in flat space. After numerical computation ofLiapunov exponents in synchronous (cosmological) time, it is shown that theBianchi I-EYM system has milder stochastic properties than the correspondingflat YM system. The Liapunov exponent is non-vanishing in conformal time.Comment: 18 pages, 6 Postscript figures, uses amsmath,amssymb,epsfig,verbatim,  to appear in CQ

Axially symmetric Bianchi I Yang - Mills cosmology as a dynamical system