On polynomials sharing preimages of compact sets, and related questions

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12 Scopus citations

Abstract

In this paper we give a solution of the following problem: under what conditions on infinite compact sets K1, K2 ⊂ C and polynomials f 1, f 2 do 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.

Original languageEnglish
Pages (from-to)163-183
Number of pages21
JournalGeometric and Functional Analysis
Volume18
Issue number1
DOIs
StatePublished - 1 Apr 2008

Keywords

  • Commuting polynomials
  • Julia sets
  • Ritt's theorems

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

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