East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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A CHARACTERIZATION OF AUTOMORPHISMS OF THE UNIT DISC BY THE POINCARÉ METRIC

  • Kang-Hyurk, Lee (Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University) ;
  • Kyu-Bo, Moon (Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University)
  • Received : 2022.09.23
  • Accepted : 2022.10.31
  • Published : 2023.01.31
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Abstract

Non-trivial automorphisms of the unit disc in the complex plane can be classified by three classes; elliptic, parabolic and hyperbolic automorphisms. This classification is due to a representation in the projective special linear group of the real field, or in terms of fixed points on the closure of the unit disc. In this paper, we will characterize this classification by the distance function of the Poincaré metric on the interior of the unit disc.

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Acknowledgement

This work was supported by Samsung Science and Technology Foundation under Project Number SSTF-BA2201-01.

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