On polynomials sharing preimages of compact sets and related questions

Details On polynomials sharing preimages of compact sets and related questions On polynomials sharing preimages of compact sets and related questions

2006-03-19

arxiv.org/abs/math/0603452v2

Mathematics

Dynamical Systems

21 pages, last version accepted by GAFA

Scientific paper

In this paper we give a solution of the following problem: under what
conditions on infinite compact sets $K_1,K_2\subset \C$ and polynomials $f_1,$
$f_2$ the preimages $f_1^{-1}\{K_1\}$ and $f_2^{-1}\{K_2\}$ 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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