Typical coexistence of infinitely many strange attractors

Abstract

We prove that the coexistence of infinitely many prevalent H\'enon-like phenomena is Kolmogorov typical in sectional dissipative $C^{d,r}$-Berger domains of parameter families of diffeomorphisms of dimension $m\geq 3$ for $d<r-1$. Namely, we answer an old question posed by Colli in [Annales de l'Institut Henri Poincare-Nonlinear Analysis, 15, 539--580 (1998)] on typicality of the coexistence of infinitely many non-hyperbolic strange attractors for $3\leq d<r-1$.