Abstract

A Herman-Avila-Bochi type formula is obtained for the average sum of the top d Lyapunov exponents over a one-parameter family of G-cocycles, where G is the group that leaves a certain, non-degenerate Hermitian form of signature (c, d) invariant. The generic example of such a group is the pseudo-unitary group U (c, d) or, in the case c = d, the Hermitian-symplectic group HSp (2d) which naturally appears for cocycles related to Schrodinger operators. In the case d = 1, the formula for HSp (2d) cocycles reduces to the Herman-Avila-Bochi formula for SL (2, R) cocycles.