Disconnected Julia set and rotation sets

Genadi Levin

Annales scientifiques de l'École Normale Supérieure (1996)

  • Volume: 29, Issue: 1, page 1-22
  • ISSN: 0012-9593

How to cite

top

Levin, Genadi. "Disconnected Julia set and rotation sets." Annales scientifiques de l'École Normale Supérieure 29.1 (1996): 1-22. <http://eudml.org/doc/82403>.

@article{Levin1996,
author = {Levin, Genadi},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {disconnected Julia set; Mandelbrot set; boundary behaviour; hyperbolic component; hedgehogs},
language = {eng},
number = {1},
pages = {1-22},
publisher = {Elsevier},
title = {Disconnected Julia set and rotation sets},
url = {http://eudml.org/doc/82403},
volume = {29},
year = {1996},
}

TY - JOUR
AU - Levin, Genadi
TI - Disconnected Julia set and rotation sets
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1996
PB - Elsevier
VL - 29
IS - 1
SP - 1
EP - 22
LA - eng
KW - disconnected Julia set; Mandelbrot set; boundary behaviour; hyperbolic component; hedgehogs
UR - http://eudml.org/doc/82403
ER -

References

top
  1. [1] V. I. ARNOLD, Geometrical methods in the theory of ordinary differential equations, Springer-Verlag, 1983. Zbl0507.34003MR84d:58023
  2. [2] L. AHLFORS and L. BERS, The Riemann mapping theorem for variable metrics (Annals of Mathematics, Vol. 72, 1960, pp. 385-404). Zbl0104.29902MR22 #5813
  3. [3] M. G. ARSOVE and G. Jr. JOHNSON, A conformal mapping technique for infinitely connected regions (Memoirs of the AMS, Vol. 91, 1970). Zbl0195.11403MR41 #7144
  4. [4] B. BRANNER, Cubic polynomials : turning around the connectedness locus, The Technical University of Denmark, Mat-report 1992-2005. 
  5. [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). Zbl0548.30021MR85m:58108
  6. [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). Zbl0668.30008MR90d:30073
  7. [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). Zbl0823.58012
  8. [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). Zbl0603.30030MR858013
  9. [9] A. DOUADY and J. H. HUBBARD, Iteration of complex quadratic polynomials (C.R.A.S., Vol. 294, 1982, pp. 123-126). Zbl0483.30014MR83m:58046
  10. [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). Zbl0587.30028MR87f:58083
  11. [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). Zbl0552.30018
  12. [12] A. EREMENKO and G. LEVIN, On periodic points of polynomials (Ukrainskii Math. Journal, v. 41, n. 11, 1989). Zbl0704.30033MR90m:58102
  13. [13] J. GUCKENHEIMER, preprint of Cornell University. 
  14. [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). Zbl0771.30028MR95d:58107
  15. [15] J. H. HUBBARD, Local connectivity of Julia sets and bifurcation loci : three theorems of J.-C. Yoccoz, preprint IHES, October 1992. 
  16. [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). Zbl0663.58018MR87k:58130
  17. [17] G. LEVIN, On Pommerenke's inequality for the eigenvalues of fixed points (Colloquium Mathematicum, Vol. LXII, fasc. 1, 1991, pp. 168-177). Zbl0742.30026MR92h:30053
  18. [18] G. LEVIN, On the complement of the Mandelbrot set (Israel Journal of Mathematics, Vol. 88, 1994, pp. 189-212). Zbl0817.30012MR96e:30058
  19. [19] G. LEVIN and F. PRZYTYCKI, External rays to periodic points (Israel Journal of Mathematics, to appear). Zbl0854.30020
  20. [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. [21] Ch. POMMERENKE, On conformal mapping and iteration of rational functions (Complex Variables, Vol. 5 (2-4), 1986, pp. 117-126). Zbl0581.30021MR87i:30045
  22. [22] C. L. PETERSEN, On the Pommerenke-Levin-Yoccoz inequality (Ergodic Theory and Dynamical Systems, Vol. 13, 1993, pp. 785-806). Zbl0802.30022MR94k:58122
  23. [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). Zbl1086.37519MR92e:58122
  24. [24] L. SARIO and M. NAKAI, Classification theory of Riemann Surfaces, Springer-Verlag, 1970. Zbl0199.40603MR41 #8660
  25. [25] P. VEERMAN, Symbolic dynamics and rotation numbers (Physica 13A, 1986, pp. 543-576). Zbl0655.58019MR88b:58107
  26. [26] J.-C. YOCCOZ, Sur la taille des membres de l'ensemble de Mandelbrot, manuscript (1987). 

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.