Distribution of postcritically finite polynomials

By C. Favre, T. Gauthier. Israel Journal of Mathematics, 2013

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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.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

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