×

Julia equivalences and abstract Siegel disks. (English) Zbl 0945.30024

Kriete, Hartje (ed.), Progress in holomorphic dynamics. Harlow: Longman. Pitman Res. Notes Math. Ser. 387, 86-101 (1998).
In order to describe the topology of the Julia set of a quadratic polynomial, Thurston has introduced a model in terms of a ’quadratic lamination’ which, in terms of an external angle, gives a locally connected model for the Julia set and its dynamics (which is not always homeomorphic to the actual Julia set), called the ’pinched disk model’. This paper is a survey about the author’s habilitation thesis which extends Thurston’s approach. This gives a different combinatorial setting in which the entire theory about the combinatorics of Julia sets and the Mandelbrot set can be re-expresssed, and it is a tool to find new combinatorial results.
For the entire collection see [Zbl 0927.00012].

MSC:

30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable
37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
PDFBibTeX XMLCite