论文标题
家庭中的lyapunov指数总和渐近
An asymptotic for sums of Lyapunov exponents in families
论文作者
论文摘要
令f_t为p^n_c的p^n_c至少2的内态性的meromorthic家族，让l（f_t）为与f_t相关的lyapunov指数的总和。 favre表明l（f_t）= l（f）\ log | t^{ - 1} |+o（\ log | t^{ - 1} |）为t-> 0，其中l（f）是通用纤维上的lyapunov指数的总和，被解释为某些投射性Berkovich空间的增强性。在对家庭的一些其他限制下，我们提供明确的错误术语。
Let f_t be a meromorphic family of endomorphisms of P^N_C of degree at least 2, and let L(f_t) be the sum of Lyapunov exponents associated to f_t. Favre showed that L(f_t)=L(f)\log|t^{-1}|+o(\log|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.
