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Degeneracy in the length spectrum for metric graphs

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Abstract

In this note we show that the length spectrum for metric graphs exhibits a very high degree of degeneracy. More precisely, we obtain an asymptotic for the number of pairs of closed geodesics (or closed cycles) with the same metric length.

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  1. School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK

    Richard Sharp

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  1. Richard Sharp
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Sharp, R. Degeneracy in the length spectrum for metric graphs. Geom Dedicata 149, 177–188 (2010). https://doi.org/10.1007/s10711-010-9475-x

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