Commuting Polynomials and Polynomials with Same Julia Set
نویسندگان
چکیده
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, Fernández, 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. §
منابع مشابه
Commuting Functions with No Common Fixed Points)
Introduction. Let/and g be continuous functions mapping the unit interval / into itself which commute under functional composition, that is, f(g(x)) = g(f(x)) for all x in /. In 1954 Eldon Dyer asked whether/and g must always have a common fixed point, meaning a point z in / for which f(z) = z=g(z). A. L. Shields posed the same question independently in 1955, as did Lester Dubins in 1956. The p...
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