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We identify a class of time-periodic linear symmetric hyperbolic equationsthat are finite codimension stable, because an associated operator has compactresolvent, sufficiently far to the right in the complex plane. This paper is anattempt to capture abstractly the observation in numerical general relativitythat some discretely self-similar spacetimes, such as Choptuik's criticalspacetime, are finite codimension stable.

Finite codimension stability of some time-periodic hyperbolic equations (via compact resolvents)