Typical coexistence of infinitely many strange attractors

TL;DR

This paper demonstrates that in certain high-dimensional dynamical systems, the coexistence of infinitely many strange attractors is a typical phenomenon, answering a longstanding question in the field.

Contribution

It proves that coexistence of infinitely many prevalent strange attractors is Kolmogorov typical in specific parameter domains of high-dimensional diffeomorphisms.

Findings

Coexistence of infinitely many strange attractors is typical in high-dimensional systems.

Answers an old open question by Colli about the typicality of non-hyperbolic attractors.

Establishes Kolmogorov typicality in sectional dissipative parameter domains.

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 $3\leq d<r-1$.