  Using the novel notion of parablender, P. Berger proved that the existence of
finitely many attractors is not Kolmogorov typical in parametric families of
diffeomorphisms. Here, motivated by the concept of Newhouse domains we define
Berger domains for families of diffeomorphisms. As an application, we show that
the coexistence of infinitely many attracting invariant smooth circles is
Kolmogorov typical in certain non-sectionally dissipative Berger domains of
parametric families in dimension three or greater.
