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Lebesgue measure of the postcritical set of neutral quadratic polynomials

Lim, Willie Rush
arXiv (All) · Papers
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dynamical-systems
We prove that the postcritical set of every quadratic polynomial with a neutral fixed point has zero Lebesgue measure. In particular, no arithmetic condition on the rotation number is required. Our proof uses sector renormalization and the pseudo-Siegel bounds of Dudko-Lyubich to derive uniform dist
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