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The correlation of length spectra of two hyperbolic surfaces

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Abstract

We derive an asymptotic formula for the number of free homotopy classes on a closed surface which have (approximately) the same length with respect to two different hyperbolic structures on the surface. The growth rate in the asymptotic formula is described in terms of the thermodynamic formalism for the geodesic flow.

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Authors and Affiliations

  1. M.S.R.I., 1000 Centennial Drive, 94720, Berkeley, CA, USA

    Richard Schwartz

  2. School of Mathematical Sciences, Queen Mary and Westifield College, University of London, Mile End Road, E1 4NS, London, UK

    Richard Sharp

Authors
  1. Richard Schwartz
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  2. Richard Sharp
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Communicated by J.-P. Eckmann

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Schwartz, R., Sharp, R. The correlation of length spectra of two hyperbolic surfaces. Commun.Math. Phys. 153, 423–430 (1993). https://doi.org/10.1007/BF02096650

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  • DOI: https://doi.org/10.1007/BF02096650

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