Abundance of strange attractors in the EBM family

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Let Λt\Lambda_t be the parameterized EBM map, and let tnt_n be the sequence appearing in the renormalization conjecture. For each natural number nn, there exists an interval InI_n contained in (1/2,tn)(1/\sqrt{2},t_n) such that Λt\Lambda_t displays at least 2n−12^{n-1} different strange attractors for parameters t∈Int\in I_n.

Strange-attractor abundance conjecture. For each natural number nn there exists an interval In⊂(1/2,tn)I_n\subset (1/\sqrt{2},t_n) such that Λt\Lambda_t displays, at least, 2n−12^{n-1} different strange attractors.

The claim predicts arbitrarily large finite multiplicity of strange attractors along the renormalization parameter intervals. The surrounding text states that these conjectures were formulated in earlier work and are proved in the present paper, so the database status is solved.

References

Primary source

Antonio Pumariño, José Ángel Rodríguez and Enrique Vigil, “Renormalization of two-dimensional piecewise linear maps: Abundance of 2-D strange attractors”, arXiv:1703.03964 (2017).

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