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A CHARACTERIZATION OF AUTOMORPHISMS OF THE UNIT DISC BY THE POINCARE ́ METRICA CHARACTERIZATION OF AUTOMORPHISMS OF THE UNIT DISC BY THE POINCARE ́ METRIC
- Other Titles
- A CHARACTERIZATION OF AUTOMORPHISMS OF THE UNIT DISC BY THE POINCARE ́ METRIC
- Issue Date
- Jan-2023
- Publisher
- 영남수학회
- Keywords
- the automorphism group; the Poincar ́e metric.
- Citation
- East Asian Mathematical Journal, v.39, no.1, pp 11 - 21
- Pages
- 11
- Indexed
- KCI
- Journal Title
- East Asian Mathematical Journal
- Volume
- 39
- Number
- 1
- Start Page
- 11
- End Page
- 21
- ISSN
- 1226-6973
2287-2833
- 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 pro- jective 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 classi- fication by the distance function of the Poincar ́e metric on the interior of the unit disc.
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