Berger domains and Kolmogorov typicality of infinitely many invariant circles.

Motivated by the classical concept of Newhouse domains (an open set of diffeomorphisms having a dense set of systems with homoclinic tangencies), we introduce formally the novel notion of Berger domains. Namely, a Berger domain is an open set of parametric families of diffeomorphisms having a dense set of families with persistent homoclinic tangencies. The original construction of Berger provides examples of such domains such that the tangencies are of codimension one and associated with sectional dissipative periodic points with real multipliers. We show that Berger domains can be constructed associated with homoclinic tangencies of arbitrarily large codimension and any type of hyperbolic periodic points. As an application, we find new Kolmogorov locally typical phenomena in dimension three or greater. Namely, we prove that generic families in a certain class of Berger domains have the phenomenon of coexistence of infinitely many attracting invariant circles for any parameter. [ABSTRACT FROM AUTHOR]