Abstract
A dynamics of quark-gluon plasmas has been defined by the evolution parameter, which at high energies depends on collision energy of atomic nuclei for appropriate multiplicities of secondary hadrons. The paper is based on the solution of evolution equation for patrons momentum distribution. A transition from regular propagation to irregular chaotic is an indicator of the quark-gluon plasma emerging. Nonlinear renormalization group equation has been solved by the method of Poincaré mappings. The equation is a model of the evolution of the momentum distribution of partons due to competing processes of their creation and fusion. As the energy increases, sequential bifurcation (doubling) of phase trajectories occurs, and scale-invariant fractal structures are to create. At sufficiently high energies of quarks and gluons, a dynamically determined quark-gluon system, corresponding to QGP, arises in space. There are also hadron-like structures. Quantum coherence effects follow by dynamic chaos. As a result, quarks and gluons merge into stable attractor structures with their subsequent decay into hadrons. The nonlinear equation introduced for quark-gluon cascade, which comprises dynamical chaos, has include effects of parton recombination. The chaotic dynamics has been connected specifically to the transverse momenta of partons. Clearly, the formation of dynamically determined stable structures should be unknown before, attractor mechanism of quark hadronization.