An asymptotic for sums of Lyapunov exponents in families
Abstract
Let ft be a meromorphic family of endomorphisms of PNC of degree at least 2, and let L(ft) be the sum of Lyapunov exponents associated to ft. Favre showed that L(ft)=L(f)|t-1|+o(|t-1|) as t -> 0, where L(f) is the sum of Lyapunov exponents on the generic fibre, interpreted as an endomorphism of some projective Berkovich space. Under some additional constraints on the family, we provide an explicit error term.
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