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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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