Title of article :
Indecomposable continua and the Julia sets of polynomials, II
Author/Authors :
Childers، نويسنده , , Douglas K. and Mayer، نويسنده , , John C. and Rogers Jr، نويسنده , , James T.، نويسنده ,
Issue Information :
دوماهنامه با شماره پیاپی سال 2006
Abstract :
We find necessary and sufficient conditions for the connected Julia set of a polynomial of degree d ⩾ 2 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.
w 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.
Keywords :
Indecomposable continuum , Principal continuum , Julia set , Complex dynamics , Prime end , Simple dense canal , Impression , Lake-of-Wada channel
Journal title :
Topology and its Applications
Journal title :
Topology and its Applications