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  • Author: Giovanni Bassanelli x
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We use pluri-potential theory to study the bifurcations of holomorphic families {ƒ λ}λ∈X of rational maps on or endomorphisms of . To this purpose we establish some formulas for L(ƒ λ) and ddcL(ƒ λ) where L(ƒ λ) is the sum of the Lyapunov exponents of ƒ λ with respect to the maximal entropy measure. We show that the bifurcation current ddcL(ƒ λ) both detects the instability of repulsive cycles and the interaction between critical and Julia sets.

For families of rational maps of degree d, we introduce a bifurcation measure defined by (ddcL(ƒ λ))2d−2 add study its first properties. In particular, we show that the support of this measure is contained in the closure of the set of rational maps having 2d − 2 distinct Cremer-Cycles. This approach yields to a purely potential-theoretic proof of Mañé-Sad-Sullivan theorem and, moreover, allows us to extend it.