On polynomials sharing preimages of compact sets and related questions
Abstract
In this paper we give a solution of the following problem: under what conditions on infinite compact sets K1,K2⊂ and polynomials f1, f2 the preimages f1-1\K1\ and f2-1\K2\ coincide. Besides, we investigate some related questions. In particular, we show that polynomials sharing an invariant compact set distinct from a point have equal Julia sets.
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