Abstract
We find several necessary and sufficient conditions for the Julia set J J of a polynomial of degree d ⩾ 2 d \geqslant 2 to be an indecomposable continuum. One condition that may be easier to check than others is the following: Suppose J J is connected; then J J is an indecomposable continuum iff the impression of some prime end of the unbounded complementary domain of J J has interior in J J .
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