FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2011/2012, VOLUME 17, NUMBER 6, PAGES 175-183

**Topological classification of Möbius transformations**

T. V. Rybalkina

V. V. Sergeichuk

Abstract

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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,
in which $$° is the composition of mappings.

Location: http://mech.math.msu.su/~fpm/eng/k1112/k116/k11605h.htm

Last modified: November 21, 2012