Distribution of polynomials with cycles of a given multiplier

Author:

Bassanelli Giovanni,Berteloot François

Abstract

AbstractIn the space of degree d polynomials, the hypersurfaces defined by the existence of a cycle of period n and multiplier e are known to be contained in the bifurcation locus. We prove that these hypersurfaces equidistribute the bifurcation current. This is a new result, even for the space of quadratic polynomials.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference17 articles.

1. Bifurcation currents in holomorphic dynamics on Pk;Bassanelli;J. Reine Angew. Math.,2007

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4. Lyapunov exponent of a rational map and multipliers of repelling cycles;Berteloot;to appear in Riv. Mat. Univ. Parma

5. On the dynamics of rational maps

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