  Given an ergodic flow $T=(T_t)_{t\in\Bbb R}$, let $I(T)$ be the set of reals
$s\ne 0$ for which the flows $(T_{st})_{t\in\Bbb R}$ and $T$ are isomorphic. It
is proved that $I(T)$ is a Borel subset of $\Bbb R^*$. It carries a natural
Polish group topology which is stronger than the topology induced from $\Bbb
R$. There exists a mixing flow $T$ such that $I(T)$ is an uncountable meager
subset of $\Bbb R^*$. For a generic flow $T$, the transformations $T_{t_1}$ and
$T_{t_2}$ are spectrally disjoint whenever $|t_1|\ne |t_2|$. A generic
transformation (i) embeds into a flow $T$ with $I(T)=\{1\}$ and (ii) does not
embed into a flow with $I(T)\ne \{1\}$. For each countable multiplicative
subgroup $S\subset\Bbb R^*$, it is constructed a Poisson suspension flow $T$
with simple spectrum such that $I(T)=S$. If $S$ is without rational relations
then there is a rank-one weakly mixing rigid flow $T$ with $I(T)=S$.
