  Competition between two main attractors of the distributed chaos, one
associated with translational symmetry (homogeneity) and another associated
with rotational symmetry (isotropy), has been studied in freely decaying
turbulence. It is shown that, unlike the case of statistically stationary
homogeneous isotropic turbulence, the attractor associated with rotational
symmetry (and controlled by Loitsyanskii integral) can dominate turbulent local
dynamics in an intermediate stage of the decay, because the attractor
associated with translational symmetry (and controlled by Birkhoff-Saffman
integral) is still not developed enough. The DNS data have been used in order
to support this conclusion.
