Bulletin of the Australian Mathematical Society

Research Article

RATIONAL MAPS ADMITTING MEROMORPHIC INVARIANT LINE FIELDS

XIAOGUANG WANGa1

a1 School of Mathematical Sciences, Fudan University, Shanghai 200433, PR of China (email: wxg688@163.com)

Abstract

It is shown that a rational map of degree at least 2 admits a meromorphic invariant line field if and only if it is conformally conjugate to either an integral Lattès map, a power map, or a Chebyshev polynomial.

(Received December 23 2008)

2000 Mathematics subject classification

  • primary 37F10; secondary 37F15

Keywords and phrases

  • invariant line field;
  • Lattès map;
  • Chebyshev polynomial

Footnotes

The research was supported by the National Natural Science Foundation of China Grant 10871047.