We consider SL(2,R)-valued cocycles over rotations of the circle and prove that they are likely to have Lyapunov exponents â‰ˆ Â± logÎ» if the norms of all of the matrices are â‰ˆ Î». This is proved for Î»â€¦ (More)

We consider some very simple examples of SL(2, R)-cocycles and prove that they have positive Lyapunov exponents. These cocycles form an open set in the C topology. Let f : (X,m) be a measureâ€¦ (More)

Multilayer interference filters having various transmission characteristics are described and compared. The emphasis is on filters with narrow stop bands such as might be used to eliminate the hazardâ€¦ (More)