  We study stationary solutions to the continuity equation for weakly
compressible flows. These describe non-equilibrium steady states of weakly
dissipative dynamical systems. Compressibility is a singular perturbation that
changes the steady state density from a constant "microcanonical" distribution
into a singular multifractal measure supported on the "strange attractor". We
introduce a representation of the latter and show that the space-averaged
properties are described universally by a log-normal distribution determined by
a single structure function. The spectrum of fractal dimensions is derived.
Application to the problem of distribution of particles in turbulence gives
testable predictions for real turbulence and stresses the role of pressure
fluctuations.
