Induced expansion for quadratic polynomials

Jacek Graczyk; Grzegorz Swiatek

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arXiv · math/9308223

Induced expansion for quadratic polynomials

Jacek Graczyk·Grzegorz Swiatek

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Abstract

We prove that non-hyperbolic non-renormalizable quadratic polynomials are expansion inducing. For renormalizable polynomials a counterpart of this statement is that in the case of unbounded combinatorics renormalized mappings become almost quadratic. Technically, this follows from the decay of the box geometry. Specific estimates of the rate of this decay are shown which are sharp in a class of S-unimodal mappings combinatorially related to rotations of bounded type. We use real methods based on cross-ratios and Schwarzian derivative complemented by complex-analytic estimates in terms of conformal moduli.

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Jacek Graczyk, Grzegorz Swiatek. 1993-08-07. Induced expansion for quadratic polynomials. https://arxiv.org/abs/math/9308223

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