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Equidistribution of critical points of the multipliers in the quadratic family

By Tanya Firsova and Igors Gorbovickis
A parameter c0Cc_0\in\mathbb C in the family of quadratic polynomials fc(z)=z2+cf_c(z)=z^2+c is a critical point of a period nn multiplier, if the map fc0f_{c_0} has a periodic orbit of period nn, whose multiplier, viewed as a locally analytic function of cc, has a vanishing derivative at c=c0c=c_0. We prove that... Show more
July 23, 2019
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Equidistribution of critical points of the multipliers in the quadratic family
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