Déformation J-équivalente de polynômes géometriquement finis

Peter Haïssinsky

Fundamenta Mathematicae (2000)

  • Volume: 163, Issue: 2, page 131-141
  • ISSN: 0016-2736

Abstract

top
Any geometrically finite polynomial f of degree d ≥ 2 with connected Julia set is accessible by structurally stable sub-hyperbolic polynomials of the same degree. Moreover, they are topologically conjugate to f on their Julia sets.

How to cite

top

Haïssinsky, Peter. "Déformation J-équivalente de polynômes géometriquement finis." Fundamenta Mathematicae 163.2 (2000): 131-141. <http://eudml.org/doc/212434>.

@article{Haïssinsky2000,
author = {Haïssinsky, Peter},
journal = {Fundamenta Mathematicae},
keywords = {Julia set; postcritical set; structurally stable polynomials; hyperbolic polynomial},
language = {fre},
number = {2},
pages = {131-141},
title = {Déformation J-équivalente de polynômes géometriquement finis},
url = {http://eudml.org/doc/212434},
volume = {163},
year = {2000},
}

TY - JOUR
AU - Haïssinsky, Peter
TI - Déformation J-équivalente de polynômes géometriquement finis
JO - Fundamenta Mathematicae
PY - 2000
VL - 163
IS - 2
SP - 131
EP - 141
LA - fre
KW - Julia set; postcritical set; structurally stable polynomials; hyperbolic polynomial
UR - http://eudml.org/doc/212434
ER -

References

top
  1. [1] L. Ahlfors, Lectures on Quasiconformal Mappings, Van Nostrand, 1966. 
  2. [2] H. Brolin, Invariant sets under iteration of rational functions, Ark. Mat. 6 (1965), 103-144. Zbl0127.03401
  3. [3] G. Cui, Geometrically finite rational maps with given combinatorics, preprint, 1997. 
  4. [4] G. David, Solutions de l’équation de Beltrami avec | | μ | | = 1 , Ann. Acad. Sci. Fenn. Ser. A I Math. 13 (1988), 25-70. Zbl0619.30024
  5. [5] A. Douady, Descriptions of compact sets in ℂ, in: Topological Methods in Modern Mathematics (Stony Brook, NY, 1991), Publish or Perish, Houston, TX, 1993, 429-465. 
  6. [6] A. Douady et J. H. Hubbard, Étude dynamique des polynômes complexes I, II, Publ. Math. Orsay 84-02 et 85-05, 1984/85. Zbl0552.30018
  7. [7] A. Douady et J. H. Hubbard, On the dynamics of polynomial-like mappings, Ann. Sci. École Norm. Sup. 18 (1985), 287-343. Zbl0587.30028
  8. [8] L. R. Goldberg and J. Milnor, Fixed points of polynomial maps. II. Fixed point portraits, ibid. 26 (1993), 51-98. Zbl0771.30028
  9. [9] P. Haïssinsky, Applications de la chirurgie holomorphe, notamment aux points paraboliques, thèse de l'Université de Paris-Sud, Orsay, 1998. 
  10. [10] P. Haïssinsky, Chirurgie parabolique, C. R. Acad. Sci. Paris 327 (1998), 195-198. 
  11. [11] R. Ma né, P. Sad and D. Sullivan, On the dynamics of rational maps, Ann. Sci. École Norm. Sup. 16 (1983), 193-217. Zbl0524.58025
  12. [12] C. T. McMullen and D. P. Sullivan, Quasiconformal homeomorphisms and dynamics III. The Teichmüller space of a holomorphic dynamical system, Adv. Math. 135 (1998), 351-395. Zbl0926.30028
  13. [13] J. Milnor, Dynamics in One Complex Variable: Introductory Lectures, Vieweg, Braunschweig, 1999. Zbl0946.30013
  14. [14] M. Shishikura, On the quasiconformal surgery of rational functions, Ann. Sci. École Norm. Sup. 20 (1987), 1-29. Zbl0621.58030

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.