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Conformal Geometry and Dynamics

ISSN 1088-4173



Nonlinear automorphisms of plane domains

Author: Timo Erkama
Journal: Conform. Geom. Dyn. 3 (1999), 151-157
MSC (1991): Primary 30D05; Secondary 58F23
Published electronically: November 30, 1999
MathSciNet review: 1725479
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Abstract: We prove that the number of holomorphic nonlinear polynomials mapping a plane domain one-to-one onto itself is at most countable.

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  • 1. Yu. V. Azarina, Invariant analytic curves for entire functions, Siberian Math. J. 30 (1989), no. 3, 349-353. MR 90j:30038
  • 2. E. M. Chirka, Complex Analytic Sets, Kluwer, 1989. MR 92b:32016
  • 3. T. Erkama, Group actions and extension problems for maps of balls, Ann. Acad. Sci. Fenn. Ser. A I Math. 556 (1973), 1-31. MR 57:624
  • 4. -, Möbius automorphisms of plane domains, Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985), 155-162. MR 87c:30063
  • 5. -, The exponential function and linearization of quadratic polynomials, Analysis, Algebra and Computers in Mathematical Research, Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, 1994, pp. 71-80. MR 95g:39028
  • 6. -, Polymorphisms and linearization of nonlinear polynomials, Ann. Acad. Sci. Fenn. Ser. A I Math. 22 (1997), 113-121. MR 97j:30008
  • 7. E. Jacobsthal, Über vertauschbare Polynome, Math. Z. 63 (1955), 243-276. MR 17:574a
  • 8. S. Lojasiewicz, Introduction to Complex Analytic Geometry, Birkhäuser, 1991. MR 92g:32002
  • 9. P. J. Myrberg, Über ganze Funktionen mit rationalem Multiplikationstheorem, Ann. Acad. Sci. Fenn. Ser. A I Math. 414 (1968), 1-20. MR 37:4256
  • 10. R. Nevanlinna, Uniformisierung, Springer, 1953. MR 15:208h

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Additional Information

Timo Erkama
Affiliation: University of Joensuu, SF-80101 Joensuu, Finland

Received by editor(s): June 23, 1999
Received by editor(s) in revised form: September 24, 1999
Published electronically: November 30, 1999
Article copyright: © Copyright 1999 American Mathematical Society

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