The Lorenz renormalization conjecture on post-critical attractors

From papers

Let ff be a Lorenz map, and let w=(w0,w1)w=(w_0,w_1) be a renormalization type. A map is infinitely ww-renormalizable when every successive renormalization is ww-renormalizable. Denote the closure of the post-critical set of ff by obreakOf obreak\mathcal{O}_f. The Lorenz renormalization conjecture. If ff is infinitely ww-renormalizable, then Of\mathcal{O}_f is a minimal Cantor attractor. For Lorenz maps, Of\mathcal{O}_f is the union of the ω\omega-limit sets of the critical values f0(c)f_0(c) and f1(c)f_1(c); the claim is known for a large class of monotone combinatorics, but remains open in general.

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Primary source

Björn Winckler, “The Lorenz Renormalization Conjecture”, arXiv:1805.01226 (2018).

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