Abstract
Linear fractional transformations on the extended complex plane are classified up to topological conjugacy. Recall that two transformations f and g are called topologically conjugate if there exists a homeomorphism h such that g = h −1 ◦ f ◦ h, where ◦ is the composition of mappings.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 17, No. 6, pp. 175–183, 2011/12.
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Rybalkina, T., Sergeichuk, V. Topological classification of Möbius transformations. J Math Sci 193, 769–774 (2013). https://doi.org/10.1007/s10958-013-1496-1
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DOI: https://doi.org/10.1007/s10958-013-1496-1