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arXiv · 2102.08316

Typical coexistence of infinitely many strange attractors

Pablo G. Barrientos·Juan David Rojas
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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 $3\leq d<r-1$.

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Pablo G. Barrientos, Juan David Rojas. 2021-02-16. Typical coexistence of infinitely many strange attractors. https://doi.org/10.1007/s00209-022-03183-5

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