  In this work we introduce the notion of an angular spectrum for a linear
discrete time nonautonomous dynamical system. The angular spectrum comprises
all accumulation points of longtime averages formed by maximal principal angles
between successive subspaces generated by the dynamical system. The angular
spectrum is bounded by angular values which have previously been investigated
by the authors. In this contribution we derive explicit formulas for the
angular spectrum of some autonomous and specific nonautonomous systems. Based
on a reduction principle we set up a numerical method for the general case; we
investigate its convergence and apply the method to systems with a homoclinic
orbit and a strange attractor. Our main theoretical result is a theorem on the
invariance of the angular spectrum under summable perturbations of the given
matrices (roughness theorem). It applies to systems with a so-called complete
exponential dichotomy (CED), a concept which we introduce in this paper and
which imposes more stringent conditions than those underlying the exponential
dichotomy spectrum.
