Hyperbolic components of polynomials with a fixed critical point of maximal order

Pascale Roesch

Annales scientifiques de l'École Normale Supérieure (2007)

  • Volume: 40, Issue: 6, page 901-949
  • ISSN: 0012-9593

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Roesch, Pascale. "Hyperbolic components of polynomials with a fixed critical point of maximal order." Annales scientifiques de l'École Normale Supérieure 40.6 (2007): 901-949. <http://eudml.org/doc/82730>.

@article{Roesch2007,
author = {Roesch, Pascale},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {component; polynomial; fixed point; critical point; Jordan curve},
language = {eng},
number = {6},
pages = {901-949},
publisher = {Elsevier},
title = {Hyperbolic components of polynomials with a fixed critical point of maximal order},
url = {http://eudml.org/doc/82730},
volume = {40},
year = {2007},
}

TY - JOUR
AU - Roesch, Pascale
TI - Hyperbolic components of polynomials with a fixed critical point of maximal order
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2007
PB - Elsevier
VL - 40
IS - 6
SP - 901
EP - 949
LA - eng
KW - component; polynomial; fixed point; critical point; Jordan curve
UR - http://eudml.org/doc/82730
ER -

References

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  1. [1] Alhfors L.V., Lectures on Quasi-Conformal Mappings, Wadsworth & Brook/Cole, Advanced Books & Software, Monterey, 1987. 
  2. [2] Blanchard P., Complex analytic dynamics on the Riemann sphere, Bull. Amer. Math. Soc.11 (1984) 85-141. Zbl0558.58017MR741725
  3. [3] Branner B., Puzzles and para-puzzles of quadratic and cubic polynomials, Proc. Symp. Appl. Math.49 (1994) 31-69. Zbl0853.58087MR1315533
  4. [4] Branner B., Hubbard J.H., The iteration of cubic polynomials, Part. 1: The global topology of the parameter space, Acta Math. 160 (1988) 143-206. Zbl0668.30008MR945011
  5. [5] Douady A., Hubbard J.H., Étude dynamique des polynômes complexes I & II, Publ. Math. d'Orsay (1984) & (1985). Zbl0552.30018
  6. [6] Douady A., Hubbard J.H., On the dynamics of polynomial-like mappings, Ann. Sci. Éc. Norm. Sup.18 (1985) 287-343. Zbl0587.30028MR816367
  7. [7] Faught D., Local connectivity in a family of cubic polynomials, Ph.D. Thesis, Cornell University, 1992. 
  8. [8] Goldberg L.R., Milnor J., Fixed points of polynomial maps. Part II. Fixed point portraits, Ann. Sci. Éc. Norm. Sup.26 (1993) 51-98. Zbl0771.30028MR1209913
  9. [9] Hubbard J.H., Local connectivity of Julia sets and bifurcation loci: three theorems of J.-C. Yoccoz, in: Goldberg L.R., Phillips V.A. (Eds.), Topological Methods in Modern Mathematics, Publish or Perish, 1993, pp. 467-511. Zbl0797.58049MR1215974
  10. [10] Levin G., Przytycki F., External rays to periodic points, Israel J. Math.94 (1996) 29-57. Zbl0854.30020MR1394566
  11. [11] Mc Mullen C., The Mandelbrot set is universal, in: Lei Tan (Ed.), The Mandelbrot Set, Theme and Variations, LMS Lecture Note Series, vol. 274, Cambridge U. Press, 2000. Zbl1062.37042MR1765082
  12. [12] Milnor J., Dynamics in One Complex Variable, Vieweg, 1999, 2nd ed. 2000. Zbl0946.30013MR1721240
  13. [13] Milnor J., Local connectivity of Julia sets: Expository lectures, in: Lei Tan (Ed.), The Mandelbrot Set, Theme and Variations, LMS Lecture Note Series, vol. 274, Cambridge U. Press, 2000, pp. 67-116. Zbl1107.37305MR1765085
  14. [14] Milnor J., On cubic polynomial maps with periodic critical point, preprint (1991), to be published dedicated to JHH. 
  15. [15] Naĭshul' V.A., Topological invariants of analytic and area-preserving mappings and their application to analytic differential equations in C 2 and C P 2 , Trans. Moscow Math. Soc.42 (1983) 239-250. Zbl0527.58035MR656288
  16. [16] Petersen C.L., On the Pommerenke–Levin–Yoccoz inequality, Ergod. Th. & Dynam. Sys.13 (1993) 785-806. Zbl0802.30022
  17. [17] Roesch P., Puzzles de Yoccoz pour les applications à allure rationnelle, L'Enseignement Mathématique45 (1999) 133-168. Zbl0977.37023MR1703365
  18. [18] Roesch P., Holomorphic motions and puzzles (following M. Shishikura), in: Lei Tan (Ed.), The Mandelbrot Set, Theme and Variations, LMS Lecture Note Series, vol. 274, Cambridge U. Press, 2000, pp. 117-132. Zbl1063.37042MR1765086
  19. [19] Słodkowski Z., Extensions of holomorphic motions, Ann. Scuola Norm. Sup. Cl. Sci.22 (1995) 185-210. Zbl0835.30012
  20. [20] Yoccoz J.-C., Petits diviseurs en dimension 1, Astérisque231 (1995). Zbl0836.30001

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