  We introduce a class of multi-scale systems with discrete time, motivated by
the problem of inviscid limit in fluid dynamics in the presence of small-scale
noise. These systems are infinite-dimensional and defined on a scale-invariant
space-time lattice. We propose a qualitative theory describing the vanishing
regularization (inviscid) limit as an attractor of the renormalization group
operator acting in the space of flow maps or respective probability kernels. If
the attractor is a nontrivial probability kernel, we say that the inviscid
limit is spontaneously stochastic: it defines a stochastic (Markov) process
solving deterministic equations with deterministic initial and boundary
conditions. The results are illustrated with solvable models: symbolic systems
leading to digital turbulence and systems of expanding interacting phases.
