Geodesic
Topological classification of Möbius transformations
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 6, pp. 175-183
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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 $g=h^{-1}\circ f\circ h$, in which $\circ$ is the composition of mappings. 
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T. V. Rybalkina; V. V. Sergeichuk. Topological classification of Möbius transformations. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 6, pp. 175-183. http://geodesic.mathdoc.fr/item/FPM_2012_17_6_a4/

[1] Budnitskaya T. V., “Klassifikatsiya topologicheski sopryazhënnykh affinnykh otobrazhenii”, Ukr. mat. zhurn., 61:1 (2009), 134–139 | MR

[2] Budnitskaya T. V., “Topologicheskaya klassifikatsiya preobrazovanii Mëbiusa”, Sb. trudov Instituta matematiki NAN Ukrainy, 6, no. 2, 2009, 349–358

[3] Markushevich A. I., Teoriya analiticheskikh funktsii, v. 1, Nachala teorii, Nauka, M., 1967 | Zbl

[4] Beardon A. F., The Geometry of Discrete Groups, Springer, New York, 1983 | MR | Zbl

[5] Blanc J., “Conjugacy classes of affine automorphisms of $\mathbb K^n$ and linear automorphisms of $\mathbb P^n$ in the Cremona groups”, Manuscripta Math., 119:2 (2006), 225–241 | DOI | MR | Zbl

[6] Budnitska T. V., “Topological classification of affine operators on unitary and Euclidean spaces”, Linear Algebra Appl., 434 (2011), 582–592 | DOI | MR | Zbl

[7] Budnitska T., Budnitska N., “Classification of affine operators up to biregular conjugacy”, Linear Algebra Appl., 434 (2011), 1195–1199 | DOI | MR | Zbl

[8] Cappell S. E., Shaneson J. L., “Nonlinear similarity of matrices”, Bull. Am. Math. Soc., 1 (1979), 899–902 | DOI | MR | Zbl

[9] Cappell S. E., Shaneson J. L., “Non-linear similarity”, Ann. Math., 113:2 (1981), 315–355 | DOI | MR | Zbl

[10] Cappell S. E., Shaneson J. L., “Non-linear similarity and linear similarity are equivariant below dimension 6”, Contemp. Math., 231 (1999), 59–66 | DOI | MR | Zbl

[11] Cappell S. E., Shaneson J. L., Steinberger M., West J. E., “Nonlinear similarity begins in dimension six”, Am. J. Math., 111 (1989), 717–752 | DOI | MR | Zbl

[12] Kuiper N. H., Robbin J. W., “Topological classification of linear endomorphisms”, Invent. Math., 19:2 (1973), 83–106 | DOI | MR | Zbl

[13] Milnor J., Dynamics in One Complex Variable, Princeton Univ. Press, Princeton, 2006 | MR

[14] Robbin J. W., “Topological conjugacy and structural stability for discrete dynamical systems”, Bull. Am. Math. Soc., 78 (1972), 923–952 | DOI | MR | Zbl