= Duistermaat-Guillemin trace formula
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For the <positive Laplace-Beltrami operator> on a <closed manifold>, the singular support of the <wave trace> lies in zero together with signed lengths of <closed geodesics>. Under the clean fixed-set hypotheses, its singularity at a periodic-geodesic length has an expansion determined by the <geodesic flow> and its linearized return map. In particular, when the relevant leading coefficient does not vanish through cancellation, that length is determined by the spectrum. The inclusion of singular supports alone does not justify an unconditional recovery of every <geodesic> length.
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