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Critical orbits of holomorphic maps on projective spaces

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Abstract

We study the dynamics of iterated holomorphic maps of a complex projective space onto itself. Relations between the Fatou set and the orbits of critical points are investigated. In particular, results concerning critically finite maps on the Riemann sphere are generalized to higher dimensional case.

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References

  1. Beardon, A.F.Iteration of Rational Functions, Springer-Verlag, Berlin, 1991.

    MATH  Google Scholar 

  2. Brolin, H. Invariant sets under iteration of rational functions,Ark. Mat.,6, 103–144, (1965).

    Article  MathSciNet  MATH  Google Scholar 

  3. Fatou, P. Sur les équations fonctionnelles,Bull. Soc. Math. France,47, 161–271, (1919);48, 33–94 and 208–314, (1920).

    MathSciNet  Google Scholar 

  4. Fornaess, J.E. and Sibony, N. Critically finite rational maps in P2,Contemporary Math.,137, 245–260, (1992).

    MathSciNet  Google Scholar 

  5. Fornaess, J.E. and Sibony, N. Complex dynamics in higher dimension I, Complex analytic methods in dynamical systems, Astérisque,222, 201–231, (1994).

    MathSciNet  Google Scholar 

  6. Fornaess, J.E. and Sibony, N. Complex dynamics in higher dimension II, Modern methods in complex analysis,Ann. of Math. Stud.,137, 135–182, (1995).

    MathSciNet  Google Scholar 

  7. Giesecke, B. Simpliziale Zerlegung abzählbarer analytischer Räume,Math. Z.,83, 177–213, (1964).

    Article  MathSciNet  MATH  Google Scholar 

  8. Grauert, H. and Remmert, R. Komplexe Räume,Math. Ann.,136, 245–318, (1958).

    Article  MathSciNet  MATH  Google Scholar 

  9. Grauert, H. and Remmert, R.Coherent Analytic Sheaves, Springer-Verlag, Berlin, 1984.

    MATH  Google Scholar 

  10. Hubbard, J. and Papadopol, P. Superattractive fixed points in Cn,Indiana Univ. Math. J.,43, 321–365, (1994).

    Article  MathSciNet  MATH  Google Scholar 

  11. Kobayashi, S.Hyperbolic Manifolds and Holomorphic Mappings, Marcel Dekker, New York, 1970.

    MATH  Google Scholar 

  12. Koopman, B.O. and Brown, A.B. On the covering of analytic loci by complexes,Trans. Am. Math. Soc.,34, 231–251, (1932).

    Article  MathSciNet  MATH  Google Scholar 

  13. Milnor, J.Dynamics in One Complex Variable: Introductory Lectures, preprint, SUNY, Stony Brook, 1990.

  14. Narasimhan, R. Several complex variables,Chicago Lectures in Math., (1971).

  15. Stein, K. Analytische Zerlegungen komplexer Räume,Math. Ann.,132, 63–93, (1956).

    Article  MathSciNet  MATH  Google Scholar 

  16. Sullivan, D. Quasiconformal homeomorphisms and dynamics I,Ann. Math.,122, 401–418, (1985).

    Article  MathSciNet  Google Scholar 

  17. Suzuki, M.Group Theory I, Springer-Verlag, Berlin, 1980.

    Google Scholar 

  18. Ueda, T. Complex dynamical systems on projective spaces, Advanced Series in Dynamical Systems,13, Chaotic Dynamical Systems,World Scientific Publ., 120–138, (1993).

  19. Ueda, T. Fatou sets in complex dynamics on projective spaces,J. Math. Soc. Japan,46, 545–555, (1994).

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Division of Mathematics, Faculty of Integrated Human Studies, Kyoto University, 606-01, Kyoto, Japan

    Tetsuo Veda

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  1. Tetsuo Veda
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Correspondence to Tetsuo Veda.

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Communicated by Eric Bedford

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Veda, T. Critical orbits of holomorphic maps on projective spaces. J Geom Anal 8, 319–334 (1998). https://doi.org/10.1007/BF02921645

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  • DOI: https://doi.org/10.1007/BF02921645

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