Geography of the cubic connectedness locus: Intertwining surgery

Annales Scientifiques de l'Ecole Normale Superieure

Volumn 32, Issue 2, 1999, Pages 151-185

  Epstein, A ^a   Yampolsky, M ^b  

^a STONY BROOK UNIVERSITY   (United States)

^b YALE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033098021     PISSN: 00129593     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-9593(99)80013-5     Document Type: Review

References (33)

1. B. Bielefeld, Changing the Order of Critical Points of Polynomials Using Quasiconformal Surgery, Thesis, Cornell. 1989.
2. B. Bielefeld, Questions in quasiconformal surgery, pp. 2-8, in Conformal Dynamics Problem List, ed. B. Bielefeld, Stony Brook IMS Preprint 1990/1, 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. 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.
4. B. Branner and N. Fagella, Homeomorphisms between Limbs of the Mandelbrot Set, MSRI Preprint 043-95.
5. 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.
6. X. Buff, Extension d'Homéomorphismes de Compacts de ℂ Manuscript, and personal communication.
7. A. Douady, Does a Julia set depend continuously on a polynomial?, Proc. of Symp. in Applied Math., Vol. 49, 1994.
8. A. Douady and J. H. Hubbard, Étude dynamique des polynômes complexes, I & II, Publ. Math. Orsay, 1984-5.
9. A. Douady and J. H. Hubbard, On the dynamics of polynomial-like mappings, Ann. Scient. Éc. Norm. Sup., 4' Série, Vol. 18, 1985, pp. 287-343.
10. A. Epstein, Counterexamples to the Quadratic Mating Conjecture, Manuscript in preparation.
11. D. Faught, Local Connectivity in a Family of Cubic Polynomials, Thesis, Cornell 1992.
12. L. Goldberg and J. Milnor, Fixed points of polynomial maps II, Ann. Scient. Éc. Norm. Sup., 4' Série, Vol. 26, 1993, pp. 51-98.
13. P. Haïssinsky, Chirurgie Croisée, Manuscript, 1996.
14. 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. J. Kiwi, Non-accessible Critical Points of Cremer Polynomials, IMS at Stony Brook Preprint 1995/2.
16. P. Lavaurs, Systèmes Dynamiques Holomorphes: Explosion de Points Périodiques, Thèse, Université de Paris-Sud, 1989.
17. O. Lehto and K. I. Virtanen, Quasiconformal Mappings in the Plane, Springer-Verlag, 1973.
18. 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.
19. M. Lyubich, On the Lebesgue Measure of a Quadratic Polynomial, IMS at Stony Brook Preprint 1991/10.
20. M. Lyubich, Dynamics of Quadratic Polynomials, I. Combinatorics and Geometry of the Yoccoz Puzzle, MSRI Preprint 026-95.
21. R. Mañé, P. Sad and D. Sullivan, On the dynamics of rational maps, Ann. Scient. Éc. Norm. Sup., 4' Série, Vol. 16, 1983, pp. 51-98.
22. C. McMullen, Complex dynamics and renormalization, Annals of Math. Studies, Princeton Univ. Press, 1993.
23. C. McMullen, Renormalization and 3-manifolds which fiber over the circle, Annals of Math. Studies, Princeton Univ. Press, 1996.
24. C. McMullen and D. Sullivan, Quasiconformal Homeomorphisms and Dynamics III: The Teichmüller Space of a Rational Map, Preprint, 1996.
25. J. Milnor, Dynamics in One Complex Variable: Introductory Lectures, IMS at Stony Brook Preprint 1990/5.
26. J. Milnor, Remarks on iterated cubic maps, Experimental Math., Vol. 1 1992, pp. 5-24.
27. J. Milnor, On Cubic Polynomials with Periodic Critical Point, Manuscript, 1991.
28. J. Milnor, Hyperbolic Components in Spaces of Polynomial Maps, with an appendix by A. Poirier, IMS at Stony Brook Preprint 1992/3.
29. J. Milnor, Periodic Orbits, External Rays and the Mandelbrot Set: An Expository Account, Preprint, 1995.
30. 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.
31. M. Shishikura, The parabolic bifurcation of rational maps, Colóquio Brasileiro de Matemática 19, IMPA, 1992.
32. R. Winters, Bifurcations in Families of Antiholomorphic and Biquadratic Maps, Thesis, Boston University, 1989.
33. B. Yarrington, Local Connectivity and Lebesgue Measure of Polynomial Julia Sets, Thesis. SUNY at Stony Brook, 1995.