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Double Cosets, Rotations and Isometric Circles

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Abstract

In this note we present an alternative to Ford’s construction of the isometric circle of a Möbius map. This construction is based on the double coset decomposition of a group, together with the action of Möbius maps on spherical and hyperbolic spaces.

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References

  1. Beardon, A.F.: The Geometry of Discrete Groups, Graduate Texts in Mathematics, vol. 91. Springer, New York (1983)

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  2. Beardon, A.F., Lorentzen, L.: Continued fractions and restrained sequences of Möbius maps. Rocky Mountain J. Math. 34, 441–466 (2004)

  3. Ford, L.R.: Automorphic Functions, 2nd edn. Chelsea Pub. Co, New York (1951)

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Authors and Affiliations

  1. Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WB, UK

    A. F. Beardon

  2. Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH, 45221-0025, USA

    D. Minda

Authors
  1. A. F. Beardon
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  2. D. Minda
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Corresponding author

Correspondence to D. Minda.

Additional information

Communicated by Pekka Koskela.

In fond memory of Walter Hayman, a kind friend, supervisor and colleague.

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Beardon, A.F., Minda, D. Double Cosets, Rotations and Isometric Circles. Comput. Methods Funct. Theory 21, 557–564 (2021). https://doi.org/10.1007/s40315-021-00375-8

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  • DOI: https://doi.org/10.1007/s40315-021-00375-8

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