Iteration of Some Birational Polynomial Maps in Pn2

  • Tomoko Shinohara
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 8)


Iteration theory of birational maps in the two dimensional complex projective space P 2 was developed mainly by Diller [1] and Nishimura [2]. Diller was inspired by works done for polynomial automorphisms of C 2, and he applied pluripotential theory to iteration theory of birational maps. On the other hand, Nishimura classified birational maps in P 2 of the form F +: [z : w : t] ↦ [f 0 : f l : t 2], where f 0, f 1 are homogeneous polynomials of degree 2. Up to a suitable conjugation of PGL(P 2), his classification table can be written as follows:


Fundamental Group Closed Curve Iteration Theory Polynomial Automorphism Large Positive Constant 
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  1. [1]
    J. Diller, Dynamics of Birational Maps of P 2, Indiana Univ. Math. J. 45, No. 3 (1996), 721–772.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    Y. Nishimura, Iteration of some birational polynomial quadratic maps of P 2, RIMS Kokyuuroku. 959 (1996), 152–167.Google Scholar
  3. [3]
    T. Ueda, M. Taniguchi and S. Morosawa, Hukuso rikigakukei josetu, Baihuukan, 1995.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Tomoko Shinohara
    • 1
  1. 1.Graduate School of Human and Environmental StudiesKyoto UniversityKyotoJapan

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