Rees-Shishikura’s theorem plays an important role in the study of matings of polynomials. It promotes Thurston’s combinatorial equivalence into a semi-conjugacy. In this work we restate and reprove Rees-Shishikura’s theorem in a more general form, which can then be applied to a wider class of postcritically finite branched coverings. We provide an application of the restated theorem.
Le théorème de Rees-Shishikura joue un rôle important dans l’étude des accouplements de polynômes. Il permet d’obtenir une semi-conjugaison à partir d’une equivalence combinatoire de Thurston. Dans ce travail, nous reformulons et redémontrons ce théorème dans un cadre plus général. Cette nouvelle version du théorème est applicable à une classe plus large de revêtements ramifiés postcritiquement finis. Nous en fournissons un exemple à la fin de notre article.
@article{AFST_2012_6_21_S5_981_0,
author = {Guizhen Cui and Wenjuan Peng and Lei Tan},
title = {On a theorem of {Rees-Shishikura}},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {981--993},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 21},
number = {S5},
year = {2012},
doi = {10.5802/afst.1359},
mrnumber = {3088264},
zbl = {1283.37050},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1359/}
}
TY - JOUR AU - Guizhen Cui AU - Wenjuan Peng AU - Lei Tan TI - On a theorem of Rees-Shishikura JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2012 SP - 981 EP - 993 VL - 21 IS - S5 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1359/ DO - 10.5802/afst.1359 LA - en ID - AFST_2012_6_21_S5_981_0 ER -
%0 Journal Article %A Guizhen Cui %A Wenjuan Peng %A Lei Tan %T On a theorem of Rees-Shishikura %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2012 %P 981-993 %V 21 %N S5 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1359/ %R 10.5802/afst.1359 %G en %F AFST_2012_6_21_S5_981_0
Guizhen Cui; Wenjuan Peng; Lei Tan. On a theorem of Rees-Shishikura. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 21 (2012) no. S5, pp. 981-993. doi : 10.5802/afst.1359. https://afst.centre-mersenne.org/articles/10.5802/afst.1359/
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