On the geometry of bifurcation currents for quadratic rational maps

François Berteloot (1) , Thomas Gauthier (2, 3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352
3 IMS - Institue for Mathematical Sciences

We describe the behaviour at infinity of the bifurcation current in the moduli space of quadratic rational maps. To this purpose, we extend it to some closed, positive (1, 1)-current on a two-dimensional complex projective space and then compute the Lelong numbers and the self-intersection of the extended current.

Domaines: Systèmes dynamiques [math.DS]

François Berteloot, Thomas Gauthier. On the geometry of bifurcation currents for quadratic rational maps. Ergodic Theory and Dynamical Systems, 2014, pp.Pages 1-11. ⟨10.1017/etds.2013.110⟩. ⟨hal-00752129⟩