A tangency condition between nested convex sets cancels the linear term in return maps, yielding quadratic contraction, super-exponential convergence to the tangency set, and fractal structures via approximately affine dynamics in log coordinates.
Preprint, arXiv:2603.28445, 2026
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The return map determines the gradient structure of the thickness function including critical points and basins, with second-order geometry via a curvature operator, but non-uniqueness from scaling and equivalences can be resolved under symmetry.
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From Tangency to Fractals: Quadratic Dynamics in Nested Convex Geometry
A tangency condition between nested convex sets cancels the linear term in return maps, yielding quadratic contraction, super-exponential convergence to the tangency set, and fractal structures via approximately affine dynamics in log coordinates.
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Inverse Problems for the Return Map in the Class ( $\mathcal{O}_C$ ): Reconstruction and Identifiability
The return map determines the gradient structure of the thickness function including critical points and basins, with second-order geometry via a curvature operator, but non-uniqueness from scaling and equivalences can be resolved under symmetry.