Bifurcation currents in holomorphic dynamics on P k
Abstract
We establish a formula for the sum of the Lyapounov exponents of an holomorphic endomorphism of
P
k
. For an holomorphic family of such endomorphisms we define the {\em bifurcation current} as
d
d
c
L
and show that it vanishes when the repulsive cycles move holomorphically. We then prove a formula which relates this current with the interaction between the Green current and the current of integration on the critical set. In the 1-dimensional case (i.e. for
P
1
) we find a geometrical description of the support of this current and its powers. Finally we introduce the {\em bifurcation measure} giving some applications. This last part may be interpreted as a generalization of Mane-Sad-Sullivan theory based on pluri-potentialist methods.