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Distribution of polynomials with cycles of a given multiplier

Published online by Cambridge University Press:  11 January 2016

Giovanni Bassanelli  and
François Berteloot
Giovanni Bassanelli
Affiliation:
Université Paul Sabatier MIG Institut de Mathématiques, de Toulouse 31062 Toulouse Cedex 9, France, berteloo@picard.ups-tlse.fr
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Abstract

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In the space of degree d polynomials, the hypersurfaces defined by the existence of a cycle of period n and multiplier eiθ 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.

Keywords

37F4532U15
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 201 , March 2011 , pp. 23 - 43
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2011

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