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Topological classification of Möbius transformations

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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Correspondence to T. Rybalkina.

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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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Keywords

  • Linear Operator
  • Conjugacy Class
  • Canonical Form
  • Discrete Dynamical System
  • Linear Fractional Transformation