Equidistribution towards the bifurcation current I : Multipliers and degree d polynomials

Thomas Gauthier (1)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352 UPJV

In the moduli space of degree d polynomials, the set Per_n(w) of classes [f] for which f admits a cycle of exact period n and multiplier w is known to be an algebraic hypersurface. We prove that, given a complex number w, these hypersurfaces equidistribute towards the bifurcation current as n tends to infinity.

Mots clés: equidistribution; bifurcation currents

Domaines: Systèmes dynamiques [math.DS]; Variables complexes [math.CV]

Thomas Gauthier. Equidistribution towards the bifurcation current I : Multipliers and degree d polynomials. 2014. ⟨hal-00922634v2⟩