Proceedings of the Second ISAAC Congress pp 1063-1070 | Cite as

# Iteration of Some Birational Polynomial Maps in Pn^{2}

Chapter

## Abstract

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:

## Keywords

Fundamental Group Closed Curve Iteration Theory Polynomial Automorphism Large Positive Constant
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## References

- [1]J. Diller,
*Dynamics of Birational Maps of***P**^{2}, Indiana Univ. Math. J. 45, No. 3 (1996), 721–772.MathSciNetMATHCrossRefGoogle Scholar - [2]Y. Nishimura,
*Iteration of some birational polynomial quadratic maps of***P**^{2}, RIMS Kokyuuroku. 959 (1996), 152–167.Google Scholar - [3]T. Ueda, M. Taniguchi and S. Morosawa,
*Hukuso rikigakukei josetu*, Baihuukan, 1995.Google Scholar

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© Kluwer Academic Publishers 2000