Local connectivity of Julia sets and bifurcation loci: three theorems of J.-C. Yoccoz. (English) Zbl 0797.58049

Goldberg, Lisa R. (ed.) et al., Topological methods in modern mathematics. Proceedings of a symposium in honor of John Milnor’s sixtieth birthday, held at the State University of New York at Stony Brook, USA, June 14-June 21, 1991. Houston, TX: Publish or Perish, Inc. 467-511+375-378 (Bilder) (1993).
Three results concerning the local connectivity of Julia sets for complex analytic polynomials are obtained. These results are closely connected with the unpublished J.-C. Yoccoz work and his lectures.
For the entire collection see [Zbl 0780.00031].


37F50 Small divisors, rotation domains and linearization in holomorphic dynamics
37F45 Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations (MSC2010)
37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable