Hyperbolicity conjecture for Molecule renormalization

Let the sped-up Molecule map be the map associated with the Molecule Renormalization, as in the source's Figure~, and let a renormalization be parametrized by this map. Molecule renormalization hyperbolicity conjecture. There is a hyperbolic renormalization with one-dimensional unstable manifolds parametrized by the sped-up Molecule map as in Figure~. This is presented as a natural extension of the cylinder-renormalization conjecture and is intended to unify satellite and neutral renormalizations; the source does not state a resolution.

Sources & referencesView supporting material

Primary source

Dzmitry Dudko, “On the MLC Conjecture and the Renormalization Theory in Complex Dynamics”, arXiv:2512.24171 (2025).

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