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arXiv · 1302.0810

Distribution of postcritically finite polynomials

Charles Favre·Thomas Gauthier
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Abstract

We prove that Misiurewicz parameters with prescribed combinatorics and hyperbolic parameters with (d - 1) distinct attracting cycles with given multipliers are equidistributed with respect to the bifurcation measure in the moduli space of degree d complex polynomials. Our proof relies on Yuan's equidistribution results of points of small heights, and uses in a crucial way Epstein's transversality results.

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Charles Favre, Thomas Gauthier. 2013-02-04. Distribution of postcritically finite polynomials. https://arxiv.org/abs/1302.0810

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