Homeomorphisms between limbs of the Mandelbrot set

Proceedings of the American Mathematical Society

Volumn 140, Issue 6, 2012, Pages 1947-1956

  Dudko, Dzmitry ^a,b   Schleicher, Dierk ^a  

^a JACOBS UNIVERSITY BREMEN   (Germany)

^b UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84857283572     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-2011-11047-5     Document Type: Article

References (20)

1. [ALS] A. Avila, M. Lyubich and W. Shein, Parapuzzle of the Multibrot set and typical dynamics of unimodal maps. Journal of the European Mathematical Society, 13 (2011), no. 1, 27-56. MR2735075
2. [BD] B. Branner, A. Douady, Surgery on complex polynomials. Holomorphic Dynamics (Mexico, 1986), 11-72, Lecture Notes in Math., 1345, Springer, Berlin, 1988. MR980952 (90e:58114)
3. [BF1] B. Branner, N. Fagella, Homeomorphisms between limbs of the Mandelbrot set. Journal of Geom. Anal. 9 (1999), 327-390. MR1757453 (2001j:37082)
4. [BF2] B. Branner, N. Fagella, Extension of homeomorphisms between limbs of the Mandelbrot set. Conform. Geom. and Dynam. 5 (2001), 100-139. MR1872159 (2002h:37076)
5. [BS] H. Bruin, D. Schleicher, Admissibility of kneading sequences and structure of Hubbard trees for quadratic polynomials. J. Lond. Math. Soc. 2 (2008), 502-522. MR2439637 (2009j:37063)
6. [Do] A. Douady, Descriptions of compact sets in C. In: Topological Methods in Modern Mathematics (Stony Brook, NY, 1991), Publish or Perish, Houston, TX (1993), 429-465. MR1215973 (94g:58185)
7. [DH] A. Douady, J.H. Hubbard, On the dynamics of polynomial-like maps. Ann. Sci. Ècole Norm. Sup. 18 (1985), 287-343. MR816367 (87f:58083)
8. [Du] D. Dudko, The decoration theorem for Mandelbrot and Multibrot sets. Preprint, arXiv:1004.0633v1 [math. DS], 2010. Submitted.
9. [Hu] J.H. Hubbard, Local connectivity of Julia sets and bifurcation loci: Three theorems of J.-C. Yoccoz. In: Topological Methods in Modern Mathematics, 467-511 and 375-378 (figures), Publish or Perish (1993). MR1215974 (94c:58172)
10. [KL1] J. Kahn, M. Lyubich, A priori bounds for some infinitely renormalizable quadratics: II. Decorations. Ann. Sci. Ec. Norm. Sup. (4) 41 (2008), no. 1, 57-84. MR2423310 (2009k:37106)
11. [KL2] J. Kahn, M. Lyubich, A priori bounds for some infinitely renormalizable quadratics: III. Molecules. In: Complex Dynamics: Families and Friends (ed. D. Schleicher), 229-254, A K Peters, Wellesley, MA (2009). MR2508259 (2010f:37078)
12. [LS] E. Lau, D. Schleicher, Internal addresses in the Mandelbrot set and irreducibility of polynomials. Preprint 19, Institute of Mathematical Sciences, Stony Brook (1994).
13. [L1] M. Lyubich, Dynamics of quadratic polynomials, I-II. Acta Math. 178 (1997), 185-297. MR1459261 (98e:58145)
14. [L2] M. Lyubich, Dynamics of quadratic polynomials, III. Parapuzzle and SBR measure. In: Géométrie complexe et systèmes dynamiques, Astérisque 261 (2000), 173-200. MR1755441 (2002e:37060)
15. [Mc] C. McMullen, Complex Dynamics and Renormalization. Ann. of Math. Stud., Princeton Univ. (1994). MR1312365 (96b:58097)
16. [Mi] J. Milnor, Periodic orbits, externals rays and the Mandelbrot set: an expository account. In: Géométrie complexe et systèmes dynamiques, Astérisque 261 (2000), 277-333. MR1755445 (2002e:37067)
17. [PR] C. L. Petersen, P. Roesch, Carrots for dessert. Preprint, arXiv:1003.3947v1 [math. DS], [2010] Submitted.
18. [Ri] J. Riedl, Arcs in Multibrot Sets, Locally Connected Julia Sets and Their Construction by Quasiconforman Surgery. Thesis, Technische Universität München, 2001, available at the Stony Brook IMS thesis server.
19. [Sch1] D. Schleicher, Internal addresses of the Mandelbrot set and Galois groups of polynomials. Preprint, arXiv:math/9411238v2 [math. DS], 1994.
20. [Sch2] D. Schleicher, On fibers and local connectivity of Mandelbrot and Multibrot sets. In: Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot. M. Lapidus, M. van Frankenhuysen (eds), Proc. Sympos. Pure Math. 72, Amer. Math. Soc. (2004), 477-517. MR2112117 (2006b:37088)