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On the n-transitivity of the group of Möbius transformations on C∞

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  • Yilmaz Özgür, Nihal

Abstract

Möbius transformations generate the conformal group in the plane and have been used in neural networks and conformal field theory. Some invariant characteristic properties of Möbius transformations such as the invariance of cross-ratio of four distinct points on the extended complex plane C∞=C∪{∞} under a Möbius transformation, have many applications. We consider the geometric interpretation of the notion of n-transitivity of the group of Möbius transformations on the extended complex plane C∞. We see that this notion is closely related to the invariant characteristic properties of Möbius transformations and the notion of cross-ratio.

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  • Yilmaz Özgür, Nihal, 2009. "On the n-transitivity of the group of Möbius transformations on C∞," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 106-110.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:1:p:106-110
    DOI: 10.1016/j.chaos.2007.07.024
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    1. El Naschie, M.S., 2006. "Holographic dimensional reduction: Center manifold theorem and E-infinity," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 816-822.
    2. Saniga, Metod, 2005. "On an observer-related unequivalence between spatial dimensions of a generic Cremonian universe," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1935-1939.
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