Geography of the cubic connectedness locus : intertwining surgery

Adam Epstein; Michael Yampolsky

Annales scientifiques de l'École Normale Supérieure (1999)

  • Volume: 32, Issue: 2, page 151-185
  • ISSN: 0012-9593

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Epstein, Adam, and Yampolsky, Michael. "Geography of the cubic connectedness locus : intertwining surgery." Annales scientifiques de l'École Normale Supérieure 32.2 (1999): 151-185. <http://eudml.org/doc/82487>.

@article{Epstein1999,
author = {Epstein, Adam, Yampolsky, Michael},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {products of Mandelbrot sets; polynomial dynamics; polynomial-like maps; fractals; quadratic polynomials; cubic polynomials; surgical tools; intertwining surgery; construction of a cubic polynomial; quasiconformal interpolation; renormalization; birenormalizable cubics; properness; injectivity; measure of the residual Julia set; discontinuity at the corner point; asymptotic geography of the cubic connectedness locus; quasiconformal surgery techniques},
language = {eng},
number = {2},
pages = {151-185},
publisher = {Elsevier},
title = {Geography of the cubic connectedness locus : intertwining surgery},
url = {http://eudml.org/doc/82487},
volume = {32},
year = {1999},
}

TY - JOUR
AU - Epstein, Adam
AU - Yampolsky, Michael
TI - Geography of the cubic connectedness locus : intertwining surgery
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1999
PB - Elsevier
VL - 32
IS - 2
SP - 151
EP - 185
LA - eng
KW - products of Mandelbrot sets; polynomial dynamics; polynomial-like maps; fractals; quadratic polynomials; cubic polynomials; surgical tools; intertwining surgery; construction of a cubic polynomial; quasiconformal interpolation; renormalization; birenormalizable cubics; properness; injectivity; measure of the residual Julia set; discontinuity at the corner point; asymptotic geography of the cubic connectedness locus; quasiconformal surgery techniques
UR - http://eudml.org/doc/82487
ER -

References

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  1. [Bi1] B. BIELEFELD, Changing the order of critical points of polynomials using quasiconformal surgery, Thesis, Cornell, 1989. 
  2. [Bi2] B. BIELEFELD, Questions in quasiconformal surgery, pp. 2-8, in Conformal Dynamics Problem List, ed. B. Bielefeld, Stony Brook IMS Preprint 1990/1991, and in part 2 of Linear and Complex Analysis Problem Book 3, ed. V. Havin and N. Nikolskii, Lecture Notes in Math., Vol. 1574, Springer-Verlag, 1994. 
  3. [BD] B. BRANNER and A. DOUADY, Surgery on complex polynomials, in Proceedings of the Symposium on Dynamical Systems, Mexico, 1986, Lecture Notes in Math., Vol. 1345, Springer-Verlag, 1987. Zbl0668.58026
  4. [BF] B. BRANNER and N. FAGELLA, Homeomorphisms between limbs of the Mandelbrot set, MSRI Preprint 043-95. 
  5. [BH] B. BRANNER and J. H. HUBBARD, The iteration of cubic polynomials. Part I : The global topology of parameter space, Acta Mathematica, Vol. 160, 1988, pp. 143-206. Zbl0668.30008MR90d:30073
  6. [Bu] X. BUFF, Extension d'homéomorphismes de compacts de ℂ, Manuscript, and personal communication. 
  7. [Do] A. DOUADY, Does a Julia set depend continuously on a polynomial ?, Proc. of Symp. in Applied Math., Vol. 49, 1994. Zbl0934.30023MR1315535
  8. [DH1] A. DOUADY and J. H. HUBBARD, Étude dynamique des polynômes complexes, I & II, Publ. Math. Orsay, 1984-1985. Zbl0552.30018
  9. [DH2] A. DOUADY and J. H. HUBBARD, On the dynamics of polynomial-like mappings, Ann. scient. Éc. Norm. Sup., 4e série, Vol. 18, 1985, pp. 287-343. Zbl0587.30028MR87f:58083
  10. [Ep] A. EPSTEIN, Counterexamples to the quadratic mating conjecture, Manuscript in preparation. 
  11. [Fa] D. FAUGHT, Local connectivity in a family of cubic polynomials, Thesis, Cornell 1992. 
  12. [GM] L. GOLDBERG and J. MILNOR, Fixed points of polynomial maps II, Ann. Scient. Éc. Norm. Sup., 4e série, Vol. 26, 1993, pp. 51-98. Zbl0771.30028MR95d:58107
  13. [Haï] P. HAÏSSINSKY, Chirurgie croisée, Manuscript, 1996. 
  14. [Hub] J. H. HUBBARD, Local connectivity of Julia sets and bifurcation loci : three theorems of J.-C. Yoccoz, in Topological methods in Modern Mathematics, Publish or Perish, 1992, pp. 467-511 and 375-378. 
  15. [Ki] J. KIWI, Non-accessible critical points of Cremer polynomials, IMS at Stony Brook Preprint 1995/2. 
  16. [La] P. LAVAURS, Systèmes dynamiques holomorphes : Explosion de points périodiques, Thèse, Université de Paris-Sud, 1989. 
  17. [LV] O. LEHTO and K. I. VIRTANEN, Quasiconformal Mappings in the Plane, Springer-Verlag, 1973. Zbl0267.30016MR49 #9202
  18. [Lyu1] M. LYUBICH, On typical behavior of the trajectories of a rational mapping of the sphere, Soviet. Math. Dokl., Vol. 27, 1983, No. 1, pp. 22-25. Zbl0595.30034MR84f:30036
  19. [Lyu2] M. LYUBICH, On the Lebesgue measure of a quadratic polynomial, IMS at Stony Brook Preprint 1991/2010. 
  20. [Lyu3] M. LYUBICH, Dynamics of quadratic polynomials, I. Combinatorics and geometry of the Yoccoz puzzle, MSRI Preprint 026-95. 
  21. [MSS] R. MAÑ;É, P. SAD and D. SULLIVAN, On the dynamics of rational maps, Ann. Scient. Éc. Norm. Sup., 4e série, Vol. 16, 1983, pp. 51-98. Zbl0524.58025
  22. [McM1] C. MCMULLEN, Complex Dynamics and Renormalization, Annals of Math. Studies, Princeton Univ. Press, 1993. 
  23. [McM2] C. MCMULLEN, Renormalization and 3-Manifolds which Fiber over the Circle, Annals of Math. Studies, Princeton Univ. Press, 1996. Zbl0860.58002MR97f:57022
  24. [McS] C. MCMULLEN and D. SULLIVAN, Quasiconformal homeomorphisms and dynamics III : The Teichmüller space of a rational map, Preprint, 1996. 
  25. [Mil1] J. MILNOR, Dynamics in one complex variable : Introductory lectures, IMS at Stony Brook Preprint 1990/1995. 
  26. [Mil2] J. MILNOR, Remarks on iterated cubic maps, Experimental Math., Vol. 1 1992, pp. 5-24. Zbl0762.58018MR94c:58096
  27. [Mil3] J. MILNOR, On cubic polynomials with periodic critical point, Manuscript, 1991. 
  28. [Mil4] J. MILNOR, Hyperbolic components in spaces of polynomial maps, with an appendix by A. Poirier, IMS at Stony Brook Preprint 1992/1993. 
  29. [Mil5] J. MILNOR, Periodic orbits, external rays and the Mandelbrot set ; An expository account, Preprint, 1995. 
  30. [NS] S. NAKANE and D. SCHLEICHER, Non-local connectivity of the tricorn and multicorns, in Proceedings of the International Conference on Dynamical Systems and Chaos, World Scientific, 1994. Zbl0989.37537
  31. [Sh] M. SHISHIKURA, The parabolic bifurcation of rational maps, Colóquio Brasileiro de Matemática 19, IMPA, 1992. 
  32. [Win] R. WINTERS, Bifurcations in families of antiholomorphic and biquadratic maps, Thesis, Boston University, 1989. 
  33. [Yar] B. YARRINGTON, Local connectivity and Lebesgue measure of polynomial Julia sets, Thesis, SUNY at Stony Brook, 1995. 

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