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Distribution of postcritically finite polynomials

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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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Authors and Affiliations

  1. Centre de Mathématiques Laurent Schwartz, École Polytechnique, 91128, Palaiseau Cedex, France

    C. Favre

  2. LAMFA UMR-CNRS 7352, Université de Picardie Jules Verne, 33 rue Saint-Leu, 80039, Amiens Cedex 1, France

    T. Gauthier

  3. Institute for Mathematical Sciences, Stony Brook University, 100 Nicolls Rd, Stony Brook, NY, 11794, USA

    T. Gauthier

Authors
  1. C. Favre
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  2. T. Gauthier
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Correspondence to C. Favre.

Additional information

First author is supported by the ERC-starting grant project “Nonarcomp” no. 307856. Both authors are supported by the ANR-Blanc project ”Lambda” ANR-13-BS01-0002

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Favre, C., Gauthier, T. Distribution of postcritically finite polynomials. Isr. J. Math. 209, 235–292 (2015). https://doi.org/10.1007/s11856-015-1218-0

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  • DOI: https://doi.org/10.1007/s11856-015-1218-0

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