Abstract
The Sacker–Sell (also called dichotomy or dynamical) spectrum \(\varSigma \) is a fundamental concept in the geometric, as well as for a developing bifurcation theory of nonautonomous dynamical systems. In general, it behaves merely upper-semicontinuously and a perturbation theory is therefore delicate. This paper explores an operator-theoretical approach to obtain invariance and continuity conditions for both \(\varSigma \) and its dynamically relevant subsets. Our criteria allow to avoid nonautonomous bifurcations due to collapsing spectral intervals and justify numerical approximation schemes for \(\varSigma \).
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