On the commuting polynomial endomorphisms of 2

Tien-Cuong Dinh[1]

  • [1] Université Paris-Sud, Mathématiques, Bâtiment 425, 91405 Orsay Cedex (France)

Annales de l’institut Fourier (2001)

  • Volume: 51, Issue: 2, page 431-459
  • ISSN: 0373-0956

Abstract

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We determine all pairs of commuting polynomial endomorphisms of 2 that extend to holomorphic endomorphisms of 2 and that have disjoint sequences of iterates.

How to cite

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Dinh, Tien-Cuong. "Sur les endomorphismes polynomiaux permutables de ${\mathbb {C}}^2$." Annales de l’institut Fourier 51.2 (2001): 431-459. <http://eudml.org/doc/115921>.

@article{Dinh2001,
abstract = {Dans cet article, nous déterminons tous les couples d’endomorphismes polynomiaux permutables de degrés supérieurs à 1 de $\{\mathbb \{C\}\}^2$ qui se prolongent en des endomorphismes holomorphes de $\{\mathbb \{P\}\}^2$ et qui possèdent deux suites d’itérés disjointes.},
affiliation = {Université Paris-Sud, Mathématiques, Bâtiment 425, 91405 Orsay Cedex (France)},
author = {Dinh, Tien-Cuong},
journal = {Annales de l’institut Fourier},
keywords = {commuting endomorphisms; orbifold; postcritically finite},
language = {fre},
number = {2},
pages = {431-459},
publisher = {Association des Annales de l'Institut Fourier},
title = {Sur les endomorphismes polynomiaux permutables de $\{\mathbb \{C\}\}^2$},
url = {http://eudml.org/doc/115921},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Dinh, Tien-Cuong
TI - Sur les endomorphismes polynomiaux permutables de ${\mathbb {C}}^2$
JO - Annales de l’institut Fourier
PY - 2001
PB - Association des Annales de l'Institut Fourier
VL - 51
IS - 2
SP - 431
EP - 459
AB - Dans cet article, nous déterminons tous les couples d’endomorphismes polynomiaux permutables de degrés supérieurs à 1 de ${\mathbb {C}}^2$ qui se prolongent en des endomorphismes holomorphes de ${\mathbb {P}}^2$ et qui possèdent deux suites d’itérés disjointes.
LA - fre
KW - commuting endomorphisms; orbifold; postcritically finite
UR - http://eudml.org/doc/115921
ER -

References

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  1. F. Berteloot, J.J. Loeb, Une caractérisation des exemples de Lattès de k  
  2. T.C. Dinh, Sur les applications de Lattès de k  Zbl1026.37040
  3. T.C. Dinh, N. Sibony, Sur les endomorphismes permutables de k  
  4. A.E. Eremenko, On some functional equations connected with iteration of rational function, Leningrad. Math. J. 1 (1990), 905-919 Zbl0724.39006MR1027462
  5. P. Fatou, Sur l'itération analytique et les substitutions permutables, J. Math. 2 (1923) Zbl50.0690.01
  6. J.E. FornÆss, N. Sibony, Complex dynamics in higher dimension I, Astérique 222 (1994), 201-213 Zbl0813.58030MR1285389
  7. G. Julia, Mémoire sur la permutabilité des fractions rationnelles, Ann. Sci. Ecole Norm. Sup. 39 (1922), 131-215 Zbl48.0364.02MR1509242
  8. S. Lamy, Alternative de Tits pour Aut [ 2 ]  Zbl1040.37031
  9. G. Levin, F. Przytycki, When do two functions have the same Julia set?, Proc. Amer. Math. Soc. 125 (1997), 2179-2190 Zbl0870.58085MR1376996
  10. J.F. Ritt, Permutable rational functions, Trans. Amer. Math. Soc. 25 (1923), 399-448 Zbl49.0246.04MR1501252
  11. D. Ruelle, Elements of differentiable dynamics and bifucation theory, Academic Press (1989) Zbl0684.58001MR982930
  12. N. Sibony, Dynamique des applications rationnelles de k , Panoramas et Synthèses 8 (1999), 97-185 Zbl1020.37026MR1760844
  13. A.P. Veselov, Integrable mappings and Lie algebras, Dokl. Akad. Nauk SSSR 292 (1987), 1289-1291 Zbl0631.32024MR880608
  14. A.P. Veselov, Integrable mappings and Lie algebras, Soviet. Math. Dokl. 35 (1987) Zbl0631.32024MR880608

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