Ergodic Theory and Dynamical Systems

Research Article

Singularities in the boundaries of local Siegel disks

James T. Rogers Jra1

a1 Department of Mathematics, Tulane University, New Orleans, LA 70118, USA

Abstract

Bounded irreducible local Siegel disks include classical Siegel disks of polynomials, bounded irreducible Siegel disks of rational and entire functions, and the examples of Herman and Moeckel. We show there are only two possibilities for the structure of the boundary of such a disk: either the boundary admits a nice decomposition onto a circle or it is an indecomposable continuum.

(Received January 03 1992)

(Revised April 20 1992)

Footnotes

† Portions of this paper were presented at the Conference and Workshop on Continuum Theory and Dynamical Systems, Lafayette, LA, 17–21 May, 1991 and at the 1991 Institute in Dynamical Systems at Boston University. This research was partially supported by a COR grant from Tulane University.