Germ-typicality of the coexistence of infinitely many sinks

In the spirit of Kolmogorov typicality, we introduce the notion of germ-typicality: in a space of dynamics, it encompasses all these phenomena that occur for a dense and open subset of parameters of any generic parametrized family contained in an open set of systems. For any 2 <= r < infinity, we prove that the Newhouse phenomenon (the coexistence of infinitely many sinks) is locally Cr-germ-typical, nearby a dissipative bicycle: a dissipative homoclinic tangency linked to a special heterodimensional cycle. During the proof we show a result of independent interest: the stabilization of some heterodimensional cycles for any regularity class r is an element of {1, ... , infinity} U {omega} by introducing a new renormalization scheme. We also continue the study of the paradynamics done in [6,7,1] and prove that parablenders appear by unfolding some heterodimensional cycles. (C) 2022 Elsevier Inc. All rights reserved.