Abstract
Given an ergodic flow T=(Tt)t∈ℝ, let I(T) be the set of reals s≠0 for which the flows (Tst)t∈ℝ and T are isomorphic. It is proved that I(T) is a Borel multiplicative subgroup of ℝ*. It carries a natural Polish group topology which is stronger than the topology induced from ℝ. There exists a mixing flow T such that I(T) is an uncountable meagre subset of ℝ*. For a generic flow T, the transformations and
are spectrally disjoint whenever |t1|≠|t2|. A generic transformation embeds into a flow T with I(T)={1}. A generic transformation does not embed into a flow with I(T)≠{1}. For each countable multiplicative subgroup S⊂ℝ*, a Poisson suspension flow T with simple spectrum is constructed such that I(T)=S. If S is without rational relations, then there is a rank-1 weakly mixing rigid flow T with I(T)=S.
