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RATIONAL MAPS ADMITTING MEROMORPHIC INVARIANT LINE FIELDS

Part of: Complex dynamical systems

Published online by Cambridge University Press:  13 August 2009

XIAOGUANG WANG
XIAOGUANG WANG*
Affiliation:
School of Mathematical Sciences, Fudan University, Shanghai 200433, PR of China (email: [email protected])
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Abstract

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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.

Keywords

invariant line fieldLattès mapChebyshev polynomial

MSC classification

Secondary: 37F10: Polynomials; rational maps; entire and meromorphic functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 80 , Issue 3 , December 2009 , pp. 454 - 461
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

References

[1]Dinh, T. C. and Sibony, N., ‘Sur les endomorphismes holomorphes permutables’, Math. Ann. 324 (2002), 33–70.CrossRefGoogle Scholar
[2]Eremenko, A., ‘Some functional equations connected with iteration of rational functions’, Algebra Anal. 1 (1989), 102–116 (in Russian). Leningrad Math. J. 1 (1990), 905–919 (in English).Google Scholar
[3]McMullen, C., Complex Dynamics and Renormalization, Annals of Mathematical Studies, 135 (Princeton University Press, Princeton, NJ, 1994).Google Scholar
[4]Milnor, J., Dynamics in One Complex Variable, 3rd edn, Annals of Mathematical Studies, 160 (Princeton University Press, Princeton, NJ, 2006).Google Scholar
[5]Milnor, J., ‘On Lattès maps’, in: Dynamics on the Riemann Sphere: A Bodil Branner Festschrift (eds. P. G. Hjorth and C. L. Peterson) (European Mathematical Society, 2006), pp. 9–43.CrossRefGoogle Scholar
[6]Ritt, J. F., ‘Permutable rational functions’, Trans. Amer. Math. Soc. 25 (1923), 398–448.CrossRefGoogle Scholar