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Distribution of postcritically finite polynomials. (English) Zbl 1352.37202
Summary: 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.

##### MSC:
 37P05 Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps 11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension 37P30 Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems
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