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

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.

     author = {Cui, Guizhen and Peng, Wenjuan and Tan, Lei},
     title = {On a theorem of Rees-Shishikura},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 21},
     number = {S5},
     year = {2012},
     pages = {981-993},
     doi = {10.5802/afst.1359},
     mrnumber = {3088264},
     zbl = {1283.37050},
     language = {en},
     url = {http://www.numdam.org/item/AFST_2012_6_21_S5_981_0}
Cui, Guizhen; Peng, Wenjuan; Tan, Lei. 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. http://www.numdam.org/item/AFST_2012_6_21_S5_981_0/

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