A Kleinian group is a finitely generated discontinuous group of linear fractional transformations 
acting on a domain in the complex
plane.
The Apollonian gasket corresponds to a limit
set that is invariant under a Kleinian group (Wolfram 2002, p. 986).
See also
Apollonian Gasket,
Linear
Fractional Transformation
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References
Ford, L. R. Automorphic Functions, 2nd ed. New York: Chelsea, 1951.Iyanaga, S. and Kawada,
Y. (Eds.). Encyclopedic
Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 425, 1980.Kra,
I. Automorphic
Forms and Kleinian Groups. Reading, MA: W. A. Benjamin, 1972.Mumford,
D.; Series, C.; and Wright, D. J. Indra's
Pearls: An Atlas of Kleinian Groups. Cambridge, England: Cambridge University
Press, 2002.Wolfram, S. A
New Kind of Science. Champaign, IL: Wolfram Media, p. 986,
2002.Referenced on Wolfram|Alpha
Kleinian Group
Cite this as:
Weisstein, Eric W. "Kleinian Group." From
MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/KleinianGroup.html
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