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.
Yoccoz, in: Topological Methods in Modern Mathematics (Stony Brook, 1991), Publish or Perish
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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.