10.1017/etds.2013.103
Sadel, Christian
Christian
Sadel0000-0001-8255-3968
A Herman-Avila-Bochi formula for higher-dimensional pseudo-unitary and Hermitian-symplectic-cocycles
Cambridge University Press
2015
2018-12-11T11:52:24Z
2019-04-26T07:22:03Z
journal_article
https://research-explorer.app.ist.ac.at/record/1503
https://research-explorer.app.ist.ac.at/record/1503.json
A Herman-Avila-Bochi type formula is obtained for the average sum of the top d Lyapunov exponents over a one-parameter family of double-struck G-cocycles, where double-struck 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 Schrödinger operators. In the case d = 1, the formula for HSp(2d) cocycles reduces to the Herman-Avila-Bochi formula for SL(2, ℝ) cocycles.