On a theorem of Rees-Shishikura
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 21 (2012) no. S5, pp. 981-993.

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.

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.

DOI : 10.5802/afst.1359
Cui, Guizhen 1 ; Peng, Wenjuan 1 ; Tan, Lei 2

1 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China
2 Département de Mathématiques Université d’Angers, Angers, 49045 France
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Cui, Guizhen; Peng, Wenjuan; Tan, Lei. On a theorem of Rees-Shishikura. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 21 (2012) no. S5, pp. 981-993. doi : 10.5802/afst.1359. http://www.numdam.org/articles/10.5802/afst.1359/

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