Disconnected Julia set and rotation sets
Levin, Genadi
Annales scientifiques de l'École Normale Supérieure, Tome 29 (1996), p. 1-22 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{ASENS_1996_4_29_1_1_0,
     author = {Levin, Genadi},
     title = {Disconnected Julia set and rotation sets},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {29},
     year = {1996},
     pages = {1-22},
     doi = {10.24033/asens.1733},
     mrnumber = {96k:30029},
     zbl = {0857.30024},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_1996_4_29_1_1_0}
}

Levin, Genadi. Disconnected Julia set and rotation sets. Annales scientifiques de l'École Normale Supérieure, Tome 29 (1996) pp. 1-22. doi : 10.24033/asens.1733. http://gdmltest.u-ga.fr/item/ASENS_1996_4_29_1_1_0/

[1] V. I. Arnold, Geometrical methods in the theory of ordinary differential equations, Springer-Verlag, 1983. | MR 84d:58023 | Zbl 0507.34003

[2] L. Ahlfors and L. Bers, The Riemann mapping theorem for variable metrics (Annals of Mathematics, Vol. 72, 1960, pp. 385-404). | MR 22 #5813 | Zbl 0104.29902

[3] M. G. Arsove and G. Jr. Johnson, A conformal mapping technique for infinitely connected regions (Memoirs of the AMS, Vol. 91, 1970). | MR 41 #7144 | Zbl 0195.11403

[4] B. Branner, Cubic polynomials : turning around the connectedness locus, The Technical University of Denmark, Mat-report 1992-2005.

[5] M. F. Barnsley, J. S. Geronimo, and A. N. Harrington, Geometrical and electrical properties of some Julia sets (Lecture Notes in Pure and Applied Mathematics, Vol. 92, 1988). | MR 85m:58108 | Zbl 0548.30021

[6] 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). | MR 90d:30073 | Zbl 0668.30008

[7] S. Bullett and P. Sentenac, Ordered orbits of the shift, square roots, and the devil's staircase (Preprint, Université Paris-Sud Mathématiques, 91-39, 1991).

[8] A. Douady, Algorithms for computing angles in the Mandelbrot set (Caotic Dynamics and Fractals, ed. Barnsley and Demko, Acad. Press, 1986, pp. 155-168). | MR 858013 | Zbl 0603.30030

[9] A. Douady and J. H. Hubbard, Iteration of complex quadratic polynomials (C.R.A.S., Vol. 294, 1982, pp. 123-126). | MR 83m:58046 | Zbl 0483.30014

[10] A. Douady and J. H. Hubbard, On the dynamics of polynomial-like mappings (Ann. École Norm. Sup., (4), Vol. 18, 1985, pp. 287-343). | Numdam | MR 87f:58083 | Zbl 0587.30028

[11] A. Douady and J. H. Hubbard, Étude dynamique des polynomes complexes I, II (Publication Mathématiques d'Orsay, no. 84-02, 1984, no. 85-04, 1985). | Zbl 0552.30018

[12] A. Eremenko and G. Levin, On periodic points of polynomials (Ukrainskii Math. Journal, v. 41, n. 11, 1989). | MR 90m:58102 | Zbl 0704.30033

[13] J. Guckenheimer, preprint of Cornell University.

[14] L. R. Goldberg and J. Milnor, Fixed Points of Polynomial Maps II. Fixed Point Portraits (Ann. Scient. École Norm. Sup., (4), Vol. 26, 1993, pp. 51-98). | Numdam | MR 95d:58107 | Zbl 0771.30028

[15] J. H. Hubbard, Local connectivity of Julia sets and bifurcation loci : three theorems of J.-C. Yoccoz, preprint IHES, October 1992.

[16] P. Lavaurs, Une description combinatoire de l'involution définie par M sur les rationnels à dénominateur impair (C.R.A.S., Vol. 303, 1986, pp. 143-146). | MR 87k:58130 | Zbl 0663.58018

[17] G. Levin, On Pommerenke's inequality for the eigenvalues of fixed points (Colloquium Mathematicum, Vol. LXII, fasc. 1, 1991, pp. 168-177). | MR 92h:30053 | Zbl 0742.30026

[18] G. Levin, On the complement of the Mandelbrot set (Israel Journal of Mathematics, Vol. 88, 1994, pp. 189-212). | MR 96e:30058 | Zbl 0817.30012

[19] G. Levin and F. Przytycki, External rays to periodic points (Israel Journal of Mathematics, to appear). | Zbl 0854.30020

[20] G. Levin and M. Sodin, Polynomials with disconnected Julia sets and Green maps (The Hebrew University of Jerusalem, preprint no. 23, 1990/1991).

[21] Ch. Pommerenke, On conformal mapping and iteration of rational functions (Complex Variables, Vol. 5 (2-4), 1986, pp. 117-126). | MR 87i:30045 | Zbl 0581.30021

[22] C. L. Petersen, On the Pommerenke-Levin-Yoccoz inequality (Ergodic Theory and Dynamical Systems, Vol. 13, 1993, pp. 785-806). | MR 94k:58122 | Zbl 0802.30022

[23] M. Sodin and P. Yuditski, The limit-periodic finite difference operator on l2 (ℤ) associated with iterations of quadratic polynomials (J. Stat. Phys., Vol. 60, 1990, pp. 863-873). | MR 92e:58122 | Zbl 01397771

[24] L. Sario and M. Nakai, Classification theory of Riemann Surfaces, Springer-Verlag, 1970. | MR 41 #8660 | Zbl 0199.40603

[25] P. Veerman, Symbolic dynamics and rotation numbers (Physica 13A, 1986, pp. 543-576). | MR 88b:58107 | Zbl 0655.58019

[26] J.-C. Yoccoz, Sur la taille des membres de l'ensemble de Mandelbrot, manuscript (1987).