Distribution of postcritically finite polynomials

C. Favre; T. Gauthier

doi:10.1007/s11856-015-1218-0

Distribution of postcritically finite polynomials

C. Favre
, T. Gauthier

Université de Picardie Jules Verne
Stony Brook University

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	235-292
Number of pages	58
Journal	Israel Journal of Mathematics
Volume	209
Issue number	1
DOIs	https://doi.org/10.1007/s11856-015-1218-0
Publication status	Published - 1 Sept 2015

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title = "Distribution of postcritically finite polynomials",

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{\textquoteright}s equidistribution results of points of small heights, and uses in a crucial way Epstein{\textquoteright}s transversality results.",

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AB - 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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JO - Israel Journal of Mathematics

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Distribution of postcritically finite polynomials

Abstract

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