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Indecomposable continua and the Julia sets of polynomials, II
- Source :
-
Topology & Its Applications . Apr2006, Vol. 153 Issue 10, p1593-1602. 10p. - Publication Year :
- 2006
-
Abstract
- Abstract: We find necessary and sufficient conditions for the connected Julia set of a polynomial of degree to be an indecomposable continuum. One necessary and sufficient condition is that the impression of some prime end (external ray) of the unbounded complementary domain of the Julia set J has nonempty interior in J. Another is that every prime end has as its impression the entire Julia set. The latter answers a question posed in 1993 by the second two authors. We show by example that, contrary to the case for a polynomial Julia set, the image of an indecomposable subcontinuum of the Julia set of a rational function need not be indecomposable. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 01668641
- Volume :
- 153
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Topology & Its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 20558987
- Full Text :
- https://doi.org/10.1016/j.topol.2004.04.013