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RATIONAL MAPS ADMITTING MEROMORPHIC INVARIANT LINE FIELDS

  • XIAOGUANG WANG (a1)
Abstract
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.

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References
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[1]Dinh T. C. and Sibony N., ‘Sur les endomorphismes holomorphes permutables’, Math. Ann. 324 (2002), 3370.
[2]Eremenko A., ‘Some functional equations connected with iteration of rational functions’, Algebra Anal. 1 (1989), 102116 (in Russian). Leningrad Math. J. 1 (1990), 905–919 (in English).
[3]McMullen C., Complex Dynamics and Renormalization, Annals of Mathematical Studies, 135 (Princeton University Press, Princeton, NJ, 1994).
[4]Milnor J., Dynamics in One Complex Variable, 3rd edn, Annals of Mathematical Studies, 160 (Princeton University Press, Princeton, NJ, 2006).
[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. 943.
[6]Ritt J. F., ‘Permutable rational functions’, Trans. Amer. Math. Soc. 25 (1923), 398448.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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