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On the geometry of bifurcation currents for quadratic rational maps

Published online by Cambridge University Press:  14 March 2014

FRANÇOIS BERTELOOT  and
THOMAS GAUTHIER
FRANÇOIS BERTELOOT
Affiliation:
Université Paul Sabatier MIG, Institut de Mathématiques de Toulouse, 31062 Toulouse Cedex 9, France email [email protected]
THOMAS GAUTHIER
Affiliation:
Université de Picardie Jules Verne, LAMFA UMR-CNRS 7352, 80039 Amiens Cedex 1, France email [email protected] Stony Brook University, Institute for Mathematical Sciences, Stony Brook, NY 11794, USA
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Abstract

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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 5 , August 2015 , pp. 1369 - 1379
Copyright
© Cambridge University Press, 2014 

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