Distribution of polynomials with cycles of a given multiplier

Giovanni Bassanelli (1) , François Berteloot (2)

1 Dipartimento di Matematica Parma
2 IMT - Institut de Mathématiques de Toulouse UMR5219

In the space of degree d polynomials, the hypersurfaces defined by the existence of a cycle of period n, and multiplier e(i theta) 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.

Domaines: Mathématiques [math]

Giovanni Bassanelli, François Berteloot. Distribution of polynomials with cycles of a given multiplier. Nagoya Mathematical Journal, 2011, 201, pp.23-43. ⟨10.1215/00277630-2010-016⟩. ⟨hal-00630907⟩