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On a theorem of Rees-Shishikura

Guizhen Cui[1]; Wenjuan Peng[1]; Lei Tan[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

Annales de la faculté des sciences de Toulouse Mathématiques (2012)

  • Volume: 21, Issue: S5, page 981-993
  • ISSN: 0240-2963

Abstract

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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.

How to cite

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Cui, Guizhen, Peng, Wenjuan, and Tan, Lei. "On a theorem of Rees-Shishikura." Annales de la faculté des sciences de Toulouse Mathématiques 21.S5 (2012): 981-993. <http://eudml.org/doc/251016>.

@article{Cui2012,
abstract = {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.},
affiliation = {Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China; Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China; Département de Mathématiques Université d’Angers, Angers, 49045 France},
author = {Cui, Guizhen, Peng, Wenjuan, Tan, Lei},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {Thurston equivalence; holomorphic dynamics; posctcritically finite branched coverings},
language = {eng},
month = {12},
number = {S5},
pages = {981-993},
publisher = {Université Paul Sabatier, Toulouse},
title = {On a theorem of Rees-Shishikura},
url = {http://eudml.org/doc/251016},
volume = {21},
year = {2012},
}

TY - JOUR
AU - Cui, Guizhen
AU - Peng, Wenjuan
AU - Tan, Lei
TI - On a theorem of Rees-Shishikura
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2012/12//
PB - Université Paul Sabatier, Toulouse
VL - 21
IS - S5
SP - 981
EP - 993
AB - 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.
LA - eng
KW - Thurston equivalence; holomorphic dynamics; posctcritically finite branched coverings
UR - http://eudml.org/doc/251016
ER -

References

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  1. Beardon (A. F.).— Iteration of rational functions, Graduate text in Mathemathics, vol. 132, Springer-Verlag, New York (1993). Zbl0742.30002MR1128089
  2. Blokh (A.) and Levin (G.).— An inequality for laminations, Julia sets and ’growing trees’, Erg. Th. and Dyn. Sys., 22, p. 63-97 (2002). Zbl1067.37058MR1889565
  3. Cui (G.), Peng (W.) and Tan (L.).— Renormalization and wandering continua of rational maps, arXiv: math/1105.2935. 
  4. Douady (A.).— Systèmes dynamiques holomorphes, (Bourbaki seminar, Vol. 1982/83) Astérisque, p. 105-106, p. 39-63 (1983). Zbl0532.30019MR728980
  5. Douady (A.) and Hubbard (J. H.).— Étude dynamique des polynômes complexes, I, II, Publ. Math. Orsay (1984-1985). Zbl0552.30018
  6. Kiwi (J.).— Rational rays and critical portraits of complex polynomials, Preprint 1997/15, SUNY at Stony Brook and IMS. MR2697078
  7. Levin (G.).— On backward stability of holomorphic dynamical systems, Fund. Math., 158, p. 97-107 (1998). Zbl0915.58089MR1656942
  8. Petersen (C. L.) and Meyer (D.).— On the notions of mating, to appear in Annales de la Faculté des Sciences de Toulouse. Zbl06167094
  9. Pilgrim (K.) and Tan (L.).— Rational maps with disconnected Julia set, Astérisque 261, volume spécial en l’honneur d’A. Douady, p. 349-384 (2000). Zbl0941.30014MR1755447
  10. Rees (M.).— A partial description of parameter space of rational maps of degree two: Part I, Acta Math., 168, p. 11-87 (1992). Zbl0774.58035MR1149864
  11. Shishikura (M.).— On a theorem of M. Rees for matings of polynomials, in The Mandelbrot set, Theme and Variations, ed. Tan Lei, LMS Lecture Note Series 274, Cambridge Univ. Press, p. 289-305 (2000). Zbl1062.37039MR1765095
  12. Tan (L.).— Matings of quadratic polynomials, Erg. Th. and Dyn. Sys., 12, p. 589-620 (1992). Zbl0756.58024MR1182664
  13. Thurston (W.).— The combinatorics of iterated rational maps (1985), published in: ”Complex dynamics: Families and Friends”, ed. by D. Schleicher, A K Peters, p. 1-108 (2008). MR2508255

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