Commuting polynomials and polynomials with same Julia set

Details Commuting polynomials and polynomials with same Julia set Commuting polynomials and polynomials with same Julia set

1995-04-26

arxiv.org/abs/math/9504210v1

Mathematics

Dynamical Systems

Scientific paper

It has been known since Julia that polynomials commuting under composition have the same Julia set. More recently in the works of Baker and Eremenko, Fern\'andez, and Beardon, results were given on the converse question: When do two polynomials have the same Julia set? We give a complete answer to this question and show the exact relation between the two problems of polynomials with the same Julia set and commuting pairs.

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