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On the topology of wandering Julia components
1. | Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China, China |
2. | Département de Mathématiques, Université d'Angers, Angers, 49045, France |
References:
[1] |
A. F. Beardon, "Iteration of Rational Functions," Springer-Verlag, New York, 1991. |
[2] |
O. Kozlovski and S. van Strien, Local connectivity and quasi-conformal rigidity of non-renormalizable polynomials, Proc. London Math. Soc., 99 (2009), 275-296.
doi: 10.1112/plms/pdn055. |
[3] |
C. T. McMullen, Automorphisms of rational maps, in "Holomorphic Functions and Moduli I" (eds. D. Drasin, C. J. Earle, F. W. Gehring, I. Kra and A. Marden), Springer, (1988), 31-60. |
[4] |
J. Milnor, "Dynamics in One Complex Variable," 3rd edition, Princeton University Press, 2006. |
[5] |
J. Milnor, On rational maps with two critical points, Experimental Mathematics, 9 (2000), 481-522. |
[6] |
K. Pilgrim and L. Tan, Rational maps with disconnected Julia set, Astérique, 261 (2000), 349-384. |
[7] |
K. Pilgrim and L. Tan, On disc-annulus surgery of rational maps, in "Proceedings of the International Conference in Dynamical Systems in Honor of Professor Liao Shan-tao 1998" (eds. Y. Jiang and L. Wen), World Scientific, (1999), 237-250. |
[8] |
W. Qiu and Y. Yin, Proof of the Branner-Hubbard conjecture on Cantor Julia sets, Sci. China Ser. A, 52 (2009), 45-65.
doi: 10.1007/s11425-008-0178-9. |
[9] |
M. Shishikura, On the quasiconformal surgery of rational functions, Ann. Sci. École Norm. Sup., 20 (1987), 1-29. |
[10] |
D. Sullivan, Quasiconformal homeomorphisms and dynamics I: Solution of the Fatou-Julia problem on wandering domains, Ann. of Math., 122 (1985), 401-418.
doi: 10.2307/1971308. |
[11] |
Y. Zhai, A generalized version of Branner-Hubbard conjecture for rational functions, Acta Mathematica Sinica, 26 (2010), 2199-2208.
doi: 10.1007/s10114-010-7632-7. |
show all references
References:
[1] |
A. F. Beardon, "Iteration of Rational Functions," Springer-Verlag, New York, 1991. |
[2] |
O. Kozlovski and S. van Strien, Local connectivity and quasi-conformal rigidity of non-renormalizable polynomials, Proc. London Math. Soc., 99 (2009), 275-296.
doi: 10.1112/plms/pdn055. |
[3] |
C. T. McMullen, Automorphisms of rational maps, in "Holomorphic Functions and Moduli I" (eds. D. Drasin, C. J. Earle, F. W. Gehring, I. Kra and A. Marden), Springer, (1988), 31-60. |
[4] |
J. Milnor, "Dynamics in One Complex Variable," 3rd edition, Princeton University Press, 2006. |
[5] |
J. Milnor, On rational maps with two critical points, Experimental Mathematics, 9 (2000), 481-522. |
[6] |
K. Pilgrim and L. Tan, Rational maps with disconnected Julia set, Astérique, 261 (2000), 349-384. |
[7] |
K. Pilgrim and L. Tan, On disc-annulus surgery of rational maps, in "Proceedings of the International Conference in Dynamical Systems in Honor of Professor Liao Shan-tao 1998" (eds. Y. Jiang and L. Wen), World Scientific, (1999), 237-250. |
[8] |
W. Qiu and Y. Yin, Proof of the Branner-Hubbard conjecture on Cantor Julia sets, Sci. China Ser. A, 52 (2009), 45-65.
doi: 10.1007/s11425-008-0178-9. |
[9] |
M. Shishikura, On the quasiconformal surgery of rational functions, Ann. Sci. École Norm. Sup., 20 (1987), 1-29. |
[10] |
D. Sullivan, Quasiconformal homeomorphisms and dynamics I: Solution of the Fatou-Julia problem on wandering domains, Ann. of Math., 122 (1985), 401-418.
doi: 10.2307/1971308. |
[11] |
Y. Zhai, A generalized version of Branner-Hubbard conjecture for rational functions, Acta Mathematica Sinica, 26 (2010), 2199-2208.
doi: 10.1007/s10114-010-7632-7. |
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