Bibliography for Mobius Transformations

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  1. Transformadas de Möbius e equações de terceiro grau
    José Carlos de Sousa Oliveira Santos
    Boletim da Sociedade Portuguesa de Matemática (nº52, Maio de 2005).  
  2. Linear Fractional Transformation Methods
    Muir Jr. J.R.
    Complex Variables, 1 January 2003, vol. 48, no. 1, pp. 69-81(13), Ingenta.  
  3. Qubit Geometry and Conformal Mapping
    Lee J-w.; Kim C.H.; Lee E.K.; Kim J.; Lee S.
    Quantum Information Processing, April 2002, vol. 1, no. 1-2, pp. 129-134(6), Ingenta.   
  4. Quaternionic linear fractional transformations and direct isometries of H5.
    Moussafir, Jacques-Olivier
    J. Geom. Phys. 37 (2001), no. 3, 183--189, MathSciNet.  
  5. The Möbius transformation, Green function and the degenerate elliptic equation.
    Ji, Xinhua
    Clifford algebras and their applications in mathematical physics, Vol. 2 (Ixtapa, 1999), 17--35, Progr. Phys., 19, Birkhäuser Boston, Boston, MA, 2000, MathSciNet.  
  6. Some properties of a linear-fractional transformation
    Kochina P.Y.; Kochina N.N.
    Journal of Applied Mathematics and Mechanics, 1999, vol. 63, no. 2, pp. 161-163(3), Ingenta.  
  7. High Speed Sound Sources Localization using Bilinear Time-frequency Transformation
    Poisson F.; Valiere J.C.; Herzog P.
    Applied Acoustics, 3 January 1998, vol. 53, no. 1, pp. 1-13(13), Ingenta.  
  8. Möbius transformations and periodic solutions of complex Riccati equations.
    Campos, Juan
    Bull. London Math. Soc. 29 (1997), no. 2, 205--215, MathSciNet.  
  9. A New Characteristic of Mobius Transformations by Use of Apollonius Points of Triangles
    Haruki H.; Rassias T.M.
    Journal of Mathematical Analysis and Applications, January 1996, vol. 197, no. 1, pp. 14-22(9), Ingenta.   
  10. Convergence of Complex Continued Fractions (in Notes)  
    John Marafino; Timothy J. McDevitt  
    Mathematics Magazine, Vol. 68, No. 3. (Jun., 1995), pp. 202-208, Jstor.  
  11. Some properties of linear-fractional transformations and the harmonic mean of matrix functions.
    Nudel'man, A. A.
    Matrix and operator valued functions, 171--184, Oper. Theory Adv. Appl., 72, Birkhäuser, Basel, 1994, MathSciNet.  
  12. The Symmetry Principle for Mobius Transformations (in Notes)  
    Louis Brickman  
    American Mathematical Monthly, Vol. 100, No. 8. (Oct., 1993), pp. 781-782, Jstor.  
  13. Iteration and bilinear transformations.  
    Short, L.
    Internat. J. Math. Ed. Sci. Tech.  24  (1993),  no. 3, 391--411, MathSciNet.  
  14. The conformal geometry of complex quadrics and the fractional-linear form of Möbius transformations.
    Robinson, Ivor; Trautman, Andrzej
    J. Math. Phys. 34 (1993), no. 11, 5391--5406, MathSciNet.  
  15. Outer compositions of hyperbolic/loxodromic linear fractional transformations.
    Gill, John
    Internat. J. Math. Math. Sci. 15 (1992), no. 4, 819--822, MathSciNet.  
  16. A convergence property for sequences of linear fractional transformations.
    Lorentzen, Lisa
    Continued fractions and orthogonal functions (Loen, 1992), 281--304, Lecture Notes in Pure and Appl. Math., 154, Dekker, New York, 1994, MathSciNet.  
  17. Conjugacy invariants of Möbius transformations.
    Wada, Masaaki
    Complex Variables Theory Appl. 15 (1990), no. 2, 125--133, MathSciNet.  
  18. Bilinear Basics (in Notes)  
    T. Hoy Booker  
    Mathematics Magazine, Vol. 62, No. 4. (Oct., 1989), pp. 262-267, Jstor.  
  19. Linear fractional transformations and companion matrices.
    Pták, Vlastimil
    Comment. Math. Univ. Carolin. 29 (1988), no. 2, 279--284, MathSciNet.  
  20. Curvature, Circles, and Conformal Maps (in Notes)  
    Alan F. Beardon  
    American Mathematical Monthly, Vol. 94, No. 1. (Jan., 1987), pp. 48-53, Jstor.  
  21. Limiting Structures for Sequences of Linear Fractional Transformations  
    Lisa Jacobsen; W. J. Thron  
    Proceedings of the American Mathematical Society, Vol. 99, No. 1. (Jan., 1987), pp. 141-146, Jstor.  
  22. Composition of Linear Fractional Transformations in Terms of Tail Sequences  
    Lisa Jacobsen  
    Proceedings of the American Mathematical Society, Vol. 97, No. 1. (May, 1986), pp. 97-104, Jstor.  
  23. A Property of Inversion in Polar Coordinates  
    Boyd, James N.
    The Math. Teach., (1985), V. 78, No. 1, pp. 60-61.
  24. An Algebraic and Geometric Approach to Two Step Iteration of Bilinear Functions (in The Teaching of Mathematics)  
    Shmuel Avital; Shlomo Libeskind  
    American Mathematical Monthly, Vol. 91, No. 1. (Jan., 1984), pp. 53-56, Jstor.  
  25. Inversion in a Circle: A Different Kind of Transformation  
    Cohen, Martin P.  
    The Math. Teach., (1983), V. 86, No. 8, pp. 620-623.
  26. Matrix Möbius transformations.
    Schwarz, Binyamin; Zaks, Abraham
    Comm. Algebra 9 (1981), no. 19, 1913--1968, MathSciNet.  
  27. Some matrix linear fractional transformations and their properties.
    Karlin, Samuel
    J. Analyse Math. 36 (1979), 145--155 (1980)
  28. Enhancing the convergence region of a sequence of bilinear transformations.
    Gill, John
    Math. Scand. 43 (1978/79), no. 1, 74--80, MathSciNet.  
  29. On discrete groups of Möbius transformations.
    Jørgensen, Troels
    Amer. J. Math. 98 (1976), no. 3, 739--749, MathSciNet.  
  30. Mobius Transformations of the Disc and One-Parameter Groups of Isometries of H^p  
    Earl Berkson; Robert Kaufman; Horacio Porta  
    Transactions of the American Mathematical Society, Vol. 199. (Nov., 1974), pp. 223-239, Jstor.  
  31. Infinite Compositions of Mobius Transformations  
    John Gill  
    Transactions of the American Mathematical Society, Vol. 176. (Feb., 1973), pp. 479-487, Jstor.  
  32. A bilinear transformation.
    Gupta, S. L.
    Math. Education 7 (1973), A41--A42, MathSciNet.  
  33. Möbius transformations in stability theory.  
    Smith, Russell A.
    Proc. Cambridge Philos. Soc.  68  1970 143--151, MathSciNet.  
  34. Transformation Geometry in the Plane by Complex Number Methods  
    Budden, F. J.  
    The Math. Gazette, (1969) V. 53, No. 383, pp. 19-31.
  35. On the Iteration of Linear Fractional Transformations  
    Nathan Eljoseph  
    American Mathematical Monthly, Vol. 75, No. 4. (Apr., 1968), pp. 362-366, Jstor.  
  36. Conformal Linear Transformations  
    Ali R. Amir-Moez  
    Mathematics Magazine, Vol. 40, No. 5. (Nov., 1967), pp. 268-270, Jstor.  
  37. The Convergence of Sequences with Linear Fractional Recurrence Relation (in Mathematical Notes)  
    Hans Liebeck  
    American Mathematical Monthly, Vol. 68, No. 4. (Apr., 1961), pp. 353-355, Jstor.  
  38. Sequences of linear fractional transformations.
    Erdös, Paul; Piranian, George
    Michigan Math. J 6 1959 205--209, MathSciNet.  
  39. The invariant circles of a bilinear transformation.
    Drazin, M. P.
    Math. Gaz. 38, (1954), MathSciNet.  
  40. A note on permutable bilinear transformations.
    Drazin, M. P.
    Math. Gaz. 36, (1952). 30--32, MathSciNet.  
  41. Note on the Arithmetic of Bilinear Transformations  
    Donald M. Adelman  
    Proceedings of the American Mathematical Society, Vol. 1, No. 4. (Aug., 1950), pp. 443-448, Jstor.  
  42. On Series of Iterated Linear Fractional Functions  
    R. D. Carmichael  
    American Journal of Mathematics, Vol. 36, No. 3. (Jul., 1914), pp. 267-288, Jstor.  

 

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